plaintext distribution ,perfect secrecy cryptosystem I have been trying to solve the next problem:
let pi be a perfect secrecy cryptosystem with specific plaintext probability distribution. 
How to prove pi will have perfect secrecy for all other possible plaintext probability distributions?
Perfect scheme \Pi defined such that for every distribution over M and every $c\in C$ it holds that:  $Pr[C=c|M=m]=Pr[C=c]$ which means that probability to get a cipher text $c$ is independent of the message been encrypted, thus independent of the distribution over the message space M.