:::::::I have no idea why you are saying all this.  Do you really think that after all the years of discussing the MHP I do not know the difference between the probability of winning by switching given the player chose door 1 and the probability of winning by switching given the player chose door 1 and the host opened door 3??? 
 :::::::The first thing we must ask when responding to the MHP is what question does the questioner intend to ask.  It is quite clear to me, from the context of the question, a column in a popular general interest magazine, that the intended question was neither of the above but that the intended question was about probability of winning by switching given the player chose any door and the host opened door another one, which hid a goat.  We know that this was indeed the intended question, so assuming the question to be about specific door numbers is perverse. 
 :::::::Now the thing that even after all this discussion you seem not to have grasped is that, even if we take the question to be asking for the probability of winning by switching given the player chose door 1 and the host opened door 3, the difference between what you call the the way popular writers and the way that mathematical writers talk about the problem is not that different.  If you really need me to explain why one more time I will.    

  
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