Show that P(A given B) = P(A intercept B) / P(B) implies the following axioms:

1.) P(A given B) = 1, where B is a subset of A

2.) If {Ai intersect B},i = 1 2 … are mutually exclusive, then

P(A1 ∪ A2 ∪… given B)= P(A1 given B)+ P(A2 given B)+…

3.) If B ⊃ H and B ⊃ G and P(G ) ≠ 0 , then

P(G )/P( H ) = P (G given B)/ P(H given B)