Conditional probabilities are just like regular probabilities that are taking into consideration that something else (a condition) already happened. We denote $\mathbf P(A \vert B)$ as the probability of [[Events]] $A$ happening, given that event $B$ already occurred. $ \mathbf P(A \vert B) = \frac{\mathbf P(A \cap B)}{\mathbf P(B)} $ We calculate a conditional probability as the overlap $\mathbf P(A \cap B)$ put into relation with the conditioned [[Sample Space]] $\mathbf P(B)$, since everything outside of the condition is already ruled out. ![[conditional-probability.png |center|300]] **Note:** A conditional probability is only defined if the conditioned sample space $P(B) >0$.