Concept - Conditional Probability

Definition (s.5): $P(A|B)$ is the probability that $A$ happens given that $B$ happens.

Example (s.6): If the patient has the symptom of toothache, conclude cavity with probability $P=P(\text{cavity}|\text{toothache})$. The slide computes it as $p(\text{cavity}\wedge \text{toothache})/p(\text{cavity})$.

Added context

The standard definition is $P(A|B)=P(A\cap B)/P(B)$, i.e. dividing by $p(\text{toothache})$; the slide as printed divides by $p(\text{cavity})$.

Used to derive Concept - Bayes Rule: $p(h|D)=p(h,D)/p(D)$ (s.13).

Related

Concept - Probability Basics, Concept - Bayes Rule, Concept - Conditional Independence

Source: 03 Text Classification - Chunk 01 (s.1-30)