How is the formula P(A|B) calculated from the probability of A and B occurring together?

In probability theory, the conditional probability of an event $A$ occurring given that event $B$ has occurred, denoted as $P(A|B)$, is calculated by dividing the probability of both events occurring together (the intersection of $A$ and $B$) by the probability of the conditioning event $B$ occurring.1

The formula is expressed as:

$$P(A|B)=\frac{P(A\cap B)}{P(B)}$$

In this equation, $P(A\cap B)$ represents the probability that both $A$ and $B$ occur, while $P(B)$ is the probability of event $B$. This calculation assumes that the probability of $B$ is not zero. This relationship is fundamental to understanding conditional probability, which is used to determine the likelihood of dependent events.1