Very probable event occuring at least once during $n$ trials Assume that Bob carries eggs from point $A$ to $B$. He can carry $1$ egg each time. Let the probability that Bob breaks an egg be $0.99999$ which is almost a certain event (for me). If Bob carries $100$ eggs separately, can we say the probability of Bob breaking an egg is $0.99999 \% = 0.00999$?
I am asking because $0.99999$ is a very high probability in my opinion, and changing the try count doesn't have any practical effect on the above example. 
 A: In probability theory, impossible events have probability $0$, but an event having probability $0$ does not guaranty it will not occur.
So a "proper" almost impossible event, according to the theory, will have probability $0$.  
Bob, as terrible as he his in holding eggs while translating in space, might surprise everyone and keep delivering intact eggs one after the other.. after the other.. after the other....
(If you dare arming him with a non depleting arsenal of eggs)
A: Just to make one more observation about "almost impossible events".  Consider the experiment of picking a random real number in the interval I := [0, 1) (say, but it's not really important, using an uniform random distribution) and the question "How probable is it that the picked number is rational"?
The set of non-rational numbers in I is uncountable, whereas the set of rational numbers in the same interval is countable.  It means that the probability of picking a non-rational number is infinitely larger than that of picking a rational number and, consequently, the probability of picking a rational number is 0.  However, nothing prevents you from picking 0.5, which is a perfectly possible result of your experiment.
As Dror points out, some events can have probability 0 and this does not mean that there is no possibility for them to occur.

What is the probability of an almost impossible event?

Mathematically speaking, it is 0.
"Almost" has a well-defined mathematical meaning.  A function can be almost everywhere continuous, meaning that it is continuous everywhere but in a countable set of places.  The Dirac Delta function is almost everywhere zero.
EDIT:
no, the explanation of "almost everywhere continuous" is not the one given in the last paragraph.  The truth is more complex than this, and the linked Wikipedia article gives a correct explanation. 
A: The probability that Bob breaking an egg is $1$ minus the probability that he breaks no eggs. For each of 100 trips, the probability of him not breaking the egg is $0.00001$. Can you conclude?
A: this is the probability that bob breaks at least one egg if he carries 100 eggs separately $1-(1-0.99999)^{100}$
