There is a 1/3 chance you picked the right answer and 2/3 chance you picked the wrong answer. It is not #3, therefore there is a 2/3 probability it is behind #2 and a 1/3 probability of being behind #1.
I don't see the math. Once 3 is eliminated, you have a 1 in 2 chance period. The original math no longer applies to the current reality.
When I use a word, Humpty Dumpty said, in a rather scornful tone, it means just what I choose it to meannothing more nor less.