When Conan then proceeded to quote Sherlock - or to quote what Doyle had written Sherlock to say as it were - the corner of John's mouth lifted up because it was a phrase he was familiar with. One that he has already heard his friend say.

"Yes well, we are living on the back of a giant turtle in another world. Fairly certain that the improbable is not out of reach in this place."

He isn't all that surprised when the following question came, asking for proof. While he does have physical proof there is also more information stored inside of that otherworldly pocketwatch that he hasn't yet shared with Conan.

"We've just been given a way to prove it. That memory I saw, the one where the woman came and claimed to be your mother, took you away from Ran and her father then held you at gunpoint. That really happened, yeah? If it is, I can show you." Once they figured out how the whole thing worked.