it's easier to think about it with 100 doors.
if you get to pick one and he opens 98 of the remaining ones, obviously you would switch to the remaining one you didnt pick, since 99/100 times the winning door will be in his set.
Is it though? Instinctively the initial choice and the last remaining door have the same odds of 1/100.
Is it though? Instinctively the initial choice and the last remaining door have the same odds of 1/100.