Real life scenario, probability model required for accidental vs supernatural causation. A = HUMAN 1
B = HUMAN 2
A is related to B, specifically A is the father of B
A goes on holiday 5 years ago, staying in a hotel in popular tourist spot near Scotland (long way from home)
During holiday and stay at hotel, B is filmed, alone, in a cut of the exterior/gardens of the hotel
(in this instance, it is to be assumed that prior to arrival at the hotel, no knowledge of a television filming)
A deceases unexpectedly (specifically early March 2010)
B is distraught A's unexpected death and is feeling pretty down and distraught as it is currently the anniversary of his death a few days previous (early March 2014)
B switches on the television, sets record/series link on a series specifically named 'The Hotel Inspector' as having B has a general interest in programs relating to regeneration, ie. turning bad into good (whether it's houses/businesses), in this scenario, "improving worst-run hotels and bed-and-breakfast establishments"
several days later, B switches on TV and decides to delete 6 out of the 10 episodes recorded as B has no interest based on synopsis of said episodes
B decides to watch the last episode which was recorded, the location is appealing to tourists
20~ minutes into watching the episode, B sees A walking through the gardens of the hotel, (like an outtake to show off the gardens of the hotel) (in the background walking), the only person in the scene was A, no interview/input from A to camera (ie. talking), just walking (destination being visually off filming/screen) A was not seen on screen again for the rest of the episode
What is the odds/probability that B having being related to A (daughter -> father) AND four years exactly to the same week A deceases, B watches TV as any other day, (although slightly upset/down in the dumps as A's aniversary of death is in less than a week away), B sees A on an episode, A being on screen for 10-20 seconds of the 1 hour program
B had NO knowledge to A being ever filmed during any holidays within A's lifetime. After some thought, B can remember A going on holiday to the small town, but A didn't reveal that he was filmed during his holiday nor is it known he was ever on television.
How likely is seeing A, since, deceased family member on a TV program, having not knowing a family member being on TV without any possible knowledge or reason to believe that they would see family member on such a unique program, and all this happening pretty much exactly 4 years to his death.
Sorry if I have over complicated/over explained this. I have tried to give you as much information as possible as i would love to have the best true answer in regards to the odds of those events taking place.
A is basically my grandad, B is my mum - she cannot believe what she saw, being spiritual, it has helped her get through the death of her father. Having seen the program, I find it unbelievable (although amazingly true) without any doubt... Although I don't believe in messages from beyond the grave. It feels like a miracle for such a rare thing to happen. I do fully understand anything can happen if the right events take place at the right times, but in this scenario, what is the probability?
Both myself and my mother really appreciate the time taken to read this and any time you can spare to help us work out how this could happen and how rare this is...
sorry if the title is misleading, I am struggling to come up with a model.
If this is the wrong place to ask this question, please could you point me in the right direction to getting the answer as it's on my mind and feel by knowing the odds/probability of the events consecutively will help me let go and accept it/understand.
If this can be worked out, could you explain the logic on how it was worked out (in an explanatory form as I am not familiar with calculus (but hoping to learn in the near future)!
I just cant stop thinking about this, thanks again
 A: Great question.  
The probability model will depend on how broad a range of facts and events is considered as the pattern in need of an explanation.  But that is essentially the question of how powerful a non-random explanation (which in this case would mean supernatural forces) is allowed as an alternative hypothesis in which different events are linked together.


*

*if the paranormal explanation is only for the recent sighting of Grandfather on television, then the filming 5 years ago is just a background fact that does not participate in the probability calculations. But,

*if you allow for supernatural orchestration of the filming so as to "plant" the images for predestined viewing 5 years later, such as influencing Grandfather to take a vacation at the right time and place and to walk exactly where a camera was pointed, then there would be two rare events to explain, which would reduce the probability, but also zillions more of non-events to dilute that. The same powers could have orchestrated anything similar during or after Grandpa's lifetime, but nothing happened until just now, and probably nothing similar will happen in the future.  If an improbable type of event with 1-in-1000000 odds happens, but does not occur in 100000 other opportunities, that is not unusual, it has odds better than 1 in 11.  

*if you consider the possibility that GrandDad was not really filmed by television (explaining why you never had heard of that before), and that his appearance on TV was actually a vision created for Mum, then any power that could arrange that could also arrange numerous more modest things like GrandDad's picture falling out of a wallet, or a beam of sunlight shining exactly on his face in a family photograph on the wall. As in the previous example, all these zillions of non-events did not happen and they probably will not happen in the future and this would undermine the improbability of the overall pattern of events and non-events. 
To keep thing simple, I'll assume the first item is what you mean.  It is given that Grandfather was filmed, by accident, and the chances of that will play no role in the estimates of probability. 
Let's say there is about a 5 percent chance that random filming of passersby is for programming that is re-broadcast periodically, that Mum and close family members' total television watching time (including recorded programs) includes at least 1 percent of what is broadcast, that there are at least 3 anniversaries (birth/death/wedding) for which a sighting within $\pm$ one week would be significant (about 1/9 of the year) and that the re-broadcast of this film will happen at least 25 times during those family members' lifetimes.  The expected number of sightings of Grandfather on television will then be 

(0.05) x (0.01) x (1/9) x 25

or slightly more than 1 in 1000.   Really it should be 1 in 50 because the probability of the film being re-broadcast is determined by the nature of the film that was part of the original accident of having been filmed, but then again maybe the film is something only to be shown once or twice, and in that case we are back to the 1 per 1000 scale of probabiliies.  It would not be much lower than that under any similar model assumptions.
