Chances (A past "Problem of the Week" problem)

You have two bags, and you put a ping-pong ball in each, marking one secretly with an X before you do so.   I take two plain, unmarked balls and insert one into each bag.  I pick a bag at random, shake it vigorously and offer it to you.  You reach in without looking and pull out a ball.  It has no X on it.  What are the chances that the X ball is in that bag?