Basicly, yes, that’s how you’d do it. There are complications (there’s a whole slew of academic papers on how to calculate this) and noone’s released an actual probability number for this collision that I’ve found, but the number was very, very small indeed. Problem now is, where you had two orbiting objects, you now have two orbiting clouds of debris, so the odds of a collision just went up quite a bit, and because it was a collision and so kinda messy, you’ve got those debris clouds spreading in random directions in both planes – so even the ISS, which is in a much higher orbit, hasn’t been ruled to be out of danger just yet. (The shuttle should be fine, but it’s not permanently in orbit so it’s easier for it to avoid trouble).

If they both have clearly-defined orbits, then it should be possible to calculate, for each of them, exactly what its probability is of being at any given point at a particular instant.

And then you just multiply the two probabilities together, resulting in a very, very, very small number.

Would that be right?