The way probability is defined as the expected value works for finite sets. The probability of getting heads is out of two possible outcomes, heads or tails. If we asked the probability out of an infinite set, like the set of positive integers, we could take a limit. For example, as this site discusses, if we ask "What is the probability of a random integer being divisible by 5?", we can still answer that question, and the answer if 1/5.
However, if we ask the question of what is the probability that of a random integer is 5, and applied the same process, we would get a limit of zero.
Is it possible to ask what is the probability that a random number is 5 in a way that makes sense mathematically?