The correct answer is Option B.
WHOSE is used when we want to know about the person to whom something belongs.
In the given sentence, the speaker is asking about the person to whom the shoes in the passageway belong.
Thus WHOSE will be the correct answer.
WHO'S is the contraction of WHO IS and thus makes the sentence grammatically incorrect.
WHICH is used to when one has to choose from the given options.
Thus Option B is the correct answer.