The probability space of the event might not be infinite (ie discrete), then the argument above fails. In the continuous (infinite) case, we consider the probability over a region since the probability of any single exact event is zero. Think of it this way, the probability of two events happening exactly the same time is zero since you are always count down further decimals like .9923534525252626 to get more accuracy and eventually the numbers will differ in a large enough decimal place. I am not sure if this answers your question.
You can think in terms of time series, which assumes that the pattern in the past will continue in the future, then the probabilities of the future changes.