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Suppose a cryptosystem achieves perfect secrecy for a particular plaintext probability distribution. Prove that perfect secrecy is maintained for any other plaintext probability distribution.

Having trouble starting this one. Just a hint to get started would be appreciated.

I am aware that a cryptosystem is said to be perfectly secure if $P(X|Y)=P(X)$ for all $x\in\mathcal{P}, y\in\mathcal{C}$

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