::::::You have to consider the decision making problem of the PLAYER. The player does not know whether or not the host chooses either door with the same probability. If the host is a computer program, the host may pick the first permissible door.  Therefore, it is very interesting to prove that the player does not need to assume anything because switching is a dominant strategy for the player. I menat to say that because lots of people write false statements about this problem, a reference to somebody else does not add authority.  The proof is self-contained and can be verified by people who took elementary probability. You may wish to consult with some mathematician at Columbia.