Given: A ≠ φ, B ≠φ

CASE 1: If we take option (A) i.e. P(A|B) = P(A).P(B)

LHS =

CASE 2: If we take option (B) i.e.

this is true, we all know that this is conditional probability.

CASE 3: If we take option C .i.e. P(A|B)×P(B|A) = 1

LHS = P(A|B) × P(B|A)

≠ RHS

Hence, the correct option is B