Well it all depends on the context. The jews didn't say "are you A Prophet?" they said :" Are you THE PROPHET" so from reading this again:
are you
(1) Elijah
(2) Christ
(3) THE PROPHET. John could be one of three but he isn't.
but how come there is no record of people asking Muhammed the questions they asked John the Baptist?
There are
As these people lived in Yathrib side by side with the Jews who often told them that a Prophet (Peace be upon him) of God was soon to come, they said to one another: "By God, this is the same thing that the Jews informed us; Lo, nobody should now get ahead of you." Thereupon they accepted his teachings and embraced Islam.