What is the probability that a position has been played before? When reading annotated games from GMs, I sometimes find annotations such as "This was tried by XXX in 1975 vs YYY". Such annotations are sometimes found very deeply in the game, sometimes past move 20.

Depending on the move number, what is the probability that my position has been previously played by someone, somewhere?
You can't calculate a percentage. But there are some interesting points to make on that topic.

1) The possibility of a position being played before goes down the more moves you make (obviously)

2) However, positions in openings with more book moves (ex. Ruy Lopez and Sicilian) come up more. 

3) If an opening was played long ago but with a terrible loss, you might be surprised how few games there are with that opening.