According to Grice's Cooperative Principle, make your contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged. Its four maxims are as follows:
The maxim of quality. Try to make your contribution one that is true, especially: (ⅰ) Do not say what you believe to be false and (ⅱ) do not say that for which you lack adequate evidence.
The maxim of quantity. (ⅰ) Make your contribution as informative as is required for the current purposes of the exchange, and (ⅱ) do not make your contribution more informative than is required.
The maxim of relevance. Make your contribution relevant.
The maxim of manner. Be perspicuous, and specially: (ⅰ) Avoid obscurity of expression; (ⅱ) Avoid ambiguity; (ⅲ) Be brief and (ⅳ) Be orderly.
In this dialogue, B observes the maxim of relevance but flouts the maxim of quantity, that is, B answers more than required in this situation and gives more information to A. A just wants to know where John is. Therefore, the conversational implicature here is that B is not sure whether John has gone to the library or not and he does not want to bear the responsibility if A does not find John.