Perfect security definitions
If M0, and M1 are any 2 m-bit messages, how is it possible that their encryption be equal b?


The definition does not say that their encryption is equal b. It says that the function f outputs b. This function is often called distinguisher (or attacker) and he should not be able to distinguish which message M0 or M1 was encrypted. In other words there exists no distinguisher who can distinguish which message was encrypted better than with probability of guessing (0.5).