Sam Harris' theory of probability on the Second Coming of Christ Sam Harris (a famous atheist) argues in an interview with Cenk Uygur that the probability of Jesus Christ coming back to Jackson County, Missouri, USA is less likely than the probability of Jesus Christ coming back anywhere on Earth. He says that it's a "mathematically true point. This is just probability theory...you're going to hear from a bunch of mathematicians who are going to insist that you grant that."
However, Cenk Uygur (also an atheist) argues that since Jesus Christ is not coming back at all (as the whole thing is "totally untrue"), then speaking about probabilities makes as much sense as dividing by zero.
Can mathematics (probability theory) be applied to a future event that might be impossible, specifically the Second Coming of Jesus Christ? If so, under what conditions/assumptions, would Sam Harris be correct?
 A: If $A$ is a subevent of $B$, then $P(A) \leq P(B)$.
Edit: As 5xum points out, Harris says that $A$ is less likely than $B$, which literally means that $P(A) < P(B)$.  This is, strictly speaking, incorrect, as it does not account for the possibility that $P(B \setminus A) = 0$.  He cannot conclude that $A$ is less likely than $B$, only that $A$ is no more likely than $B$.
A: There are many possible probability measures that could allow us to meaningfully compare probabilities of probability zero events, using something like the Radon-Nikodym derivative. (After a little reading, I have found that there is a general statistical construction called the conditional probability distribution that fits the bill nicely.)
To take the first example that popped into my head, suppose that $P(x)$ is a continuous probability distribution function on $\mathbb{R}_{\geq 0}$ such that $\int_{0}^\epsilon P(x) dx$ is the probability that somebody will appear with genetic distance at most $\epsilon$ from Jesus.  Then (by our assumptions about the distribution) there must be zero probability that Jesus Himself will appear.
But nevertheless, we could have $P(0) > 0$ (and I would guess that we do, given my many encounters with people similar to Jesus).  Given some other distribution $Q$ (like the weighted distribution function for Jackson County), we could imagine calculating that $P(0) >> Q(0)$ very explicitly.
This is a meaningful way to numerically compare the relative probabilities of the various impossible appearances of Jesus, so Cenk Uygur has clearly jumped to conclusions, most likely from an inadequate foundation in Lebesgue integration and measure theory.
His "like dividing by zero" comment further suggests that he has never even heard of the Dirac delta measure!  I find his willingness to comment on such sensitive mathematical matters an appalling abuse of the interviewer's chair, and I insist that he recuse himself from the public stage until he has done something to address these foundational statistical deficiencies.
At my university, even first-year graduate students in statistics should be able to compare impossible events with ease.  There is really no excuse for these standards, especially from celebrities.
A: I side with Cenk Uygur here, Sam Harris' argument is not good math.
Harris is probably referring to the fact that P(A ∧ B) ≤ P(A), but that rule is only relevant if you already have a probabilistic model for your system. 
However, here they are talking about which probabilistic model is the right one. Harris is succumbing to the issue Laplace tried to describe in his "sunrise problem". If you assume a probabilistic model where there is a constant probability p that the sun rises each day, you can use Bayes theorem (as Laplace did) combined with the observation that the sun rose every day you are alive (10000 days, say) to show that the probability that the sun will NOT rise tomorrow is 1/10001. However, this is clearly nonsense, as we have a much better physical model of the solar system from which we know that the probability that the sun will rise is pretty much 100%. 
By Harris' logic, the 'uniform probability' model is more likely because it simply predicts whether or not the sun will rise. In contrast our solar system model not only predicts whether it will rise, but also the precise time at which it will rise, and is thus is less believable. This illustrates that the fact that a model makes more precise predictions does not make it more wrong.
Really, the issue Sam and Cenk are discussing is a "model selection" problem, specifically for the three models of Atheism, Christianity and Mormonism. Model selection is not math, it is philosophy, as you can read in the link. Sam's position is not mathematically justified.
A: *

*There is no way to prove that God* does not exist with 100% certainty.

*Thus, the existence of God is possible and has a non-zero probability, however small.

*Then it follows that the event of God bringing back Jesus Christ anywhere on Earth is also possible and has a non-zero probability.

*Therefore, the probability of God bringing back Jesus Christ to a specific location on Earth (Jackson County, Missouri) has a smaller probability than God bringing back Jesus Christ to any possible location on Earth.

*So, Sam Harris is correct.


*An omniscient, omnipotent, omnipresent, omni-everything God, of course
