Thank you. I've updated my initial guess of p(critical bugs | did not find critical bugs) from 0.5 to 0.82 given my estimate of likelihood and base rates.

If you've looked, it is. The more and the better you look, the better evidence it is.

If a test almost always finds something, then the failure of that test to find something is strong evidence.

s/evidence/proof/.

Evidence of absence ("we searched really carefully and nothing came up") does update the Bayesian priors significantly, so the probability of absence of bugs can now be estimated as much higher.