Infinity and absolute probability

A friend and myself are arguing about the probability of the least probable (1/infinity) outcome given infinite chances.

The whole argument revolves around the premise the universe is finite. Because it is finite, occurences of events with low probabilities (such as 1/infinity) may never occur. However, if the universe was infinite then everything would always occur.

I'm not sure how to mathematically represent this so here is what I've done simply:

P(x) = 1/infinity

t = infinity

P*t = 1

Is this true? Could someone explain this if I am wrong? Thanks!