If a probability is more than zero, it will probably happen given infinity.
More precisely, if the probability of an event is more than zero, it will occur with probability approaching one as the number of repeated trials increases without limit.
I'm familiar with the joke proof that 1 = 2, but thanks for the laugh.
You need to add, "If the events are independent."
This is one of the Borel-Cantelli lemmas. (Wikipedia's entry is correct here; I checked.)