The probability of the two remaining doors is not equal, I now realise, because you have the extra piece of info that a losing door was removed after your first choice.
Chance first door wins=1 in 3
Chance second choice wins=chance first door loses=1- (1/3)=2/3
Chance first door wins=1 in 3
Chance second choice wins=chance first door loses=1- (1/3)=2/3