SOLUTION: If P(A) > 0, P(B) > 0 and P(A) < P(A|B), show that P(B) < P(B|A) Thank you.

By the definition, the conditional probability is


    P(A|B) = .


So, you are given that 


    P(A) < .


Multiply both side of this inequality by the positive ratio  .     You will get then  


    P(B) < .


But the right side is  P(B|A).   Hence,


    P(B) < P(B|A).


It is exactly what has to be proved.