Cryptography Question from Katz and Lindell Book Introduction to Modern Cryptography

From Let E = (Gen, Enc, Dec) over message space M be an encryption scheme that achieves perfect secrecy. Let M1 M, M2 =M/M1 be two subsets of M such that |M1| 1, |M2| 1. Furthermore, let D1 be a distribution over M1, D2 be a distribution over M2. Finally, let C1 (resp. C2) be the random variable corresponding to the distribution over ciphertexts when messages are sampled from D1 (resp. D2), and let C1 (resp.C2) be the corresponding ciphertext spaces.

Is it possible that there exists a ciphertext c C1 C2 such that Pr[C1=c] =/= Pr[C2=c]? If yes, give an example of a specific encryption scheme that is perfectly secret and for which the above holds. If not, prove that for any encryption scheme that is perfectly secret, the above cannot hold.