Original sentence: A different approach to solving the problem, commonly used in mathematical sources, uses the knowledge of the number of the opened door, and hence treats it as a conditional probability problem—explicitly addressing the probability in the example case where the host opens Door 3 after the player initially chooses Door 1
Edited sentence: A different approach to solving the problem, often used in mathematical sources (though there is nothing unmathematical about the simple solution to the simple version of the problem), uses the knowledge of the number of the opened door, and hence treats it as a conditional probability problem—explicitly addressing the probability in the example case where the host opens Door 3 after the player initially chooses Door 1.Both questions have the same numerical answer, 2/3, but the interpretation of the relevant probability is different; and the proof that the answer is correct is more involved when one asks a more refined question.More precisely one could say there are two different and both more or less standard mathematical interpretations of the question, one asking for an unconditional and the other for a conditional probability.The more refined question needs more assumptions to be made in order to fix the solution