By adding constraints such as human lifespan, you change the calculation from an infinite set to a bounded set, which means you are now working with a different problem.

Given a non-zero event probability, as the set size approaches infinity the probability of a single occurrence within the set approaches 1.

Measuring the probability that an event will occur in a single test is different than measuring the probability that an event will occur in a set of tests. Even though the latter depends on the former, you're measuring separate probabilities because the former does not depend on the number of tests performed.