Definition:Conditional Probability

Definition
Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $A, B \in \Sigma$ be events of $\EE$.

We write the conditional probability of $A$ given $B$ as $\map \Pr {A \mid B}$, and define it as:
 * the probability that $A$ has occurred, given that $B$ has occurred.

Also see

 * Chain Rule for Probability, where it is shown that $\map \Pr {A \mid B} = \dfrac {\map \Pr {A \cap B} } {\map \Pr B}$.