I don't even know how they got at it, but it sounds like a typical wild guess to me. How would you even arrive at that figure?

Here is a contemporary paper discussing the risk, which doesn't seem to come up with the 3e-6 number, and here are some of Hamming's reflections. An excerpt from the second link:

Shortly before the first field test (you realize that no small scale experiment can be done--either you have a critical mass or you do not), a man asked me to check some arithmetic he had done, and I agreed, thinking to fob it off on some subordinate. When I asked what it was, he said, "It is the probability that the test bomb will ignite the whole atmosphere." I decided I would check it myself!

Compton claims (in an interview with Pearl Buck I cannot easily find online) that 3e-6 was actually the decision criterion (if it was higher than that, they were going to shut down the project as more dangerous than the Nazis), and the estimate came in at lower, and so they went ahead with the project.

In modern reactors, they try to come up with a failure probability by putting distributions on unknown variables during potential events, simulating those events, and then figuring out what portion of the joint input distribution will lead to a catastrophic failure. One could do the same with unknown parameters like the cross-section of nitrogen at various temperatures; "this is what we think it could be, and we only need to be worried if it's over here."