Thought of that and discarded but they are three independent events (chances) and have independent outcomes. First event has a probability of 1:2900 second then has a 1:2899 probability and the third has 1:2898. Each chance reduces the pool by the winning chance assuming it's not thrown back in to win again.

It's like flipping a coin; 1:2 odds that it's heads. The odds for the next flip, 1:2 no different and so on. The increased odds comes about when one says what are the odds that 2 heads comes up in 2 tries which if math serves me, the odds are 1:4.