Actually it's only approximately 1 in 720,000. (Assuming there is only 3 versions of 'Polly').

We are playing the whole playlist, so at sometime we will find the first version. We don't care which version it is, or where in the playlist it is. The odds of it being there are 1 in 1.

The question is about which tracks follow. Now we are looking for 1 of 2 tracks out of 1200, without caring which of the 2 we find. Odds of 1 in 600. Finally we need one track out of 1200.

So 1/600 * 1/1200 = 1/720,000.

It's not worth bothering about adjusting for 1199, 1198 etc. He said 'over 1200' tracks, so worrying about this is pointless. He could have 120000 tracks for all we know, which makes our error extreme. Of course, the context suggests that he has just over 1200 tracks, but you get the point..