Which Twin has the Tony?

[PairTheBoard]

Two girls are identical twins. One was born first so is technically the older of the two. One of the girls has a Tony haircut while the other does not. We do not know which girl has the Tony and have no reason to think one is more likely than the other to have the Tony. One girl is behind door #1 and the other is behind door #2 with a 50-50 chance for either to be behind either door.

Now, door #1 is opened to show that the twin behind it has the Tony haircut. What is the probabilty that the girl behind door #2 is the older twin?

PairTheBoard