In a box, I have a ball, which has an unknown colour (can be either red or blue). I put in another ball, which is red, shake the box and take out a random ball. The ball taken out turns out to be red. If I take out the another ball, what is the chance of drawing a red ball?

Right after I read that question, I'm thinking the answer is 50%. The problem is, I have to have some sort of written proof. Can someone help me with that?