A probability function is defined as an additive normalized measure over the algebra: a function      \[ P: {\cal S} \rightarrow [0, 1] \]    such that \(P(R \cup Q) = P(R) + P(Q)\) if \(R \cap Q = \emptyset\) and \(P(W) = 1\). The conditional probability \(P(Q \mid R)\) is defined as  \[ P(Q \mid R) \; = \; \frac{P(Q \cap R)}{P(R)} , \]  whenever \(P(R) &gt; 0\). It determines the relative size of the set \(Q\) within the set \(R\). It is often read as the probability of the event \(Q\) given that the event \(R\) occurs. Recall that the set \(R\) consists of all samples \(s\) that include a record of the event associated with \(R\). By looking at \(P(Q \mid R)\) we zoom in on the probability function within this set \(R\), i.e., we consider the condition that the associated event occurs.