I'm fail to see how step 2 leads to step 3. The fact that there are less woman programmers overall should not have any affect on P(good|woman,programmer).
I can't figure out why you would use such an algorithm though. Most people who want to hire programmers look at their resumes from people who have self-selected as programmers (possibly on a job search forum) and interview them. If you decide there are not enough programmers you might hire people at random ("would you be willing to learn to be a programmer if paid?" "yes" "hired, you start Monday") - there might be factors to exclude some people because they can never be great programmers, but I'm not aware of what such factors might be - gender doesn't seem to be one though.
In the real world, incompetence may not be a huge hurdle when selling complex systems. Also, these biases are invisible, until one thinks about them or spots them in the wild.
Of being a programmer, not being a good programmer. There are more men than women in programming, but the recruiters want to tell good programmers from bad ones, not programmers from nurses. The data clearly shows that a randomly chosen man is more likely to be a programmer than a randomly chosen woman, but that's irrelevant. The likelihood that a randomly chosen female programmer is good should be about the same as the likelihood that a randomly chosen male programmer is good, and that's what hiring managers care about.
You're correct that there should not be any affect.
The problem is that many systems are designed such that there is an affect.