You don't get condensation after you shut down.

You get it when you first start up and all of the metal in the exhaust is cold, the combustion gasses cool down real quick. The left pipe is longer so it cools down the gasses more.
A lot of exhaust systems have the majority of the exhaust pushed out the right pipe and so it takes even longer to heat up the left pipe.
As stated there is a lot of water vapor as part of the exhaust gas and when it cools below 212 degrees F, it turns back into water.