Conditional probability is expressed as P(A|B), which represents the probability of event A occurring given that event B has occurred. The formula P(A|B) = P(A ∩ B) / P(B) illustrates this relationship, where P(A ∩ B) is the probability of both A and B happening together. Visualizing this with a Venn Diagram helps clarify that the relevant sample space is limited to event B, focusing on the intersection of A and B. Understanding this concept involves recognizing that the probability of A is now conditional on the occurrence of B. Drawing out the Venn Diagram can aid in grasping these ideas more clearly.