The way I read it, the comma "," means "given", so what they write p(a, b) would be written as the conditional probability p(a|b) in contemporary CS/math litera

The way I read it, the comma "," means "given", so what they write p(a, b) would be written as the conditional probability p(a|b) in contemporary CS/math literature. h <- e means (h OR (NOT E)), which is the usual meaning of implication (either the consequent is true or the antecedent is false) So p(h <- e GIVEN e) = p((h OR (NOT e)) GIVEN e) = p(h GIVEN e) since NOT e is false given that e is true.