Counters

A bag contains one counter, which has a 50/50 chance of being black or white. A white counter is put in, the bag shaken, and a counter drawn out, which proves to be white. What is now the chance of drawing a white counter?

Please comment on this post to propose an answer.
Answer in approximately one week.

NB :- I do enjoy puzzles, and I have written my own for a bit of fun on a MUD I used to frequent, but I'm far too busy/lazy to write my own for the purposes of this blog, which is intended as a bit of fun for regular readers of plep and anyone else who may happen by (though I may well recycle some of the puzzles I wrote all those years ago). I'm sure you could find the answer on the WWW with a bit of searching skill (this is an old puzzle - very old, in fact), but solving the puzzle by yourself is far more fun, believe me!