Selection probability + time variable?

#1
Greetings statisticians,

I seek advice regarding a probability of selection. Here is the scenario: I, living in the US, have a music collection totaling 1000 CDs. A friend, living in Southeast Asia, has a collection totaling 2000 CDs. Given that we have similar musical interests yet live in different time zones, what is the probability that, without each other's knowledge, we will choose to listen to the same album on the same day, and at the same time? In my statistical ignorance, part of me says the answer would simply be x out of 3000. Another part of me, however, is convinced that the time factor may exponentially compound the likelihood of this happening. My goal is to come up with as exact a number as possible to represent this coincidence. This is not for homework purposes, but merely for my own edification: I would like to include this figure as part of an anecdote in a review of the album in question.

Many thanks for any help you all can offer!
Tyran
 
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