At Mark S.'s recommendation, I am posting this as an answer.
Often, the set of possible something or rather is the set of all relevant objects under some restriction. So given the situation, all plaintexts which satisfy your restriction are in P. For example, if Bob has no number '$0$' on his keyboard, the possible plaintexts are those using all numbers except $0$. The plaintext $101$ is impossible, as there would be no way for him to write it.
More generally, mathematicians have a concept of 'existence,' which just means there is no logical contradiction in an object satisfying certain properties. For example, we say that an even prime number exists, since $2$ certainly is both even and prime. Hence the set of possible objects are those which exist given a set of constraints. The set of all possible even prime numbers is just $\{2\}$.