Bugs can be absolutely pathological.
This is very true. I simplified the information a bit because I was posting about the math as a matter of intellectual curiosity, not to get help debugging. I have a model of what was causing the crash that I find reasonably convincing, which I outlined in my response to jimrandomh, below. So, while it's a real-world problem, for purposes of math we can assume that the effect of commenting out the line is an indication of a point bug, as it were. I found the Bayes confusing anyway, so there's no need to complexify further. :)
Thanks for the math answer; I need to think about it carefully to absorb it fully, but I thought I'd respond to the programming answer first.
I have successfully confused myself about probability again.
I am debugging an intermittent crash; it doesn't happen every time I run the program. After much confusion I believe I have traced the problem to a specific line (activating my debug logger, as it happens; irony...) I have tested my program with and without this line commented out. I find that, when the line is active, I get two crashes on seven runs. Without the line, I get no crashes on ten runs. Intuitively this seems like evidence in favour of the hypothesis that the line is causing the crash. But I'm confused on how to set up the equations. Do I need a probability distribution over crash frequencies? That was the solution the last time I was confused over Bayes, but I don't understand what it means to say "The probability of having the line, given crash frequency f", which it seems I need to know to calculate a new probability distribution.
I'm going to go with my intuition and code on the assumption that the debug logger should be activated much later in the program to avoid a race condition, but I'd like to understand this math.