The mathematics of uncertainty
How do you assign a number to "how likely"? Andrey Kolmogorov showed that the entire theory rests on just three rules. Every other formula you'll use is a consequence of these.
In words: probabilities are never negative; the probability that something happens is exactly 1; and for events that can't overlap, probabilities simply add. That's it. A probability is a way of splitting the total mass 1 across the outcomes.
Picture a whole pie cut into slices, one slice per outcome. No slice can have negative size (that is the rule P(A) ≥ 0), and all the slices together must fill the entire pie, never more and never less, which is exactly P(Ω) = 1. Asking for the probability of an event just means adding up the slices that belong to it.