Well, this is back again...causing arguments! If you don't agree with the conclusion in the video, I hope the way I see it helps...
Try looking at this in a group format with two groups, A and B. Group A has a single door (the one the contestant chose) and group B has the remaining two. It should be clear that there is a 1/3 chance the prize is in group A and a 2/3 chance the prize is in group B. When the host eliminates one of the doors in group B, the contestant is being done a favor by being told the reaming door in group B has the 2/3 chance of having the prize that could formerly only be applied to the group as a whole.
Try looking at this in a group format with two groups, A and B. Group A has a single door (the one the contestant chose) and group B has the remaining two. It should be clear that there is a 1/3 chance the prize is in group A and a 2/3 chance the prize is in group B. When the host eliminates one of the doors in group B, the contestant is being done a favor by being told the reaming door in group B has the 2/3 chance of having the prize that could formerly only be applied to the group as a whole.
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