It is an equivalent problem. kqr's comment is wrong in its implications. Whether you open one door or 998 doors, you are revealing information about the likelih

It is an equivalent problem. kqr's comment is wrong in its implications. Whether you open one door or 998 doors, you are revealing information about the likelihood of what is behind the last door. It's just more obvious that this is the case when N-2 doors are opened than just one.