This topic is covered pretty well in introductory probability courses. Basically, we accept the fact that each event is in truth deterministic, but that the forces that determine the outcome are unknowable and random. We build a mathematical model that expresses the distribution of events (a likelihood function) and use it to determine with what frequency a particular event will occur.

I'd also add that the inability to predict when such a event will occur is the precise reason that makes poker a game worth playing.