Probability theory only makes sense in the context of
- Fully observable
- Fully deterministic
system such as a coin, dice or a deck of cards.
In this context probability is nothing but a partitioning - bucket-sorting of proven to be possible well-defined and fully-determined events with "buckets" of different "size".
Applied to cards or roulette wheels (or game theory in general) it shines. Applied to a weather forecasting (or financial markets) it is a modern astrology.