Earlier quoted context omitted.
In your extreme example you can see that people in the B' group (those who don't have black hair) can be safely excluded as suspects. So even in this artificial example you can see that knowing P(B|A) is of value.
You seem to have missed the part where the extreme example is not real life. If you exclude people without black hair from suspicion, then the baddies will find someone without black hair. You cannot assume P(B|A) will not be modified by the policies you adopt. ...well, you can if you are the TSA and don't actually have to answer to anybody.... P(B|A) will never be 100% anyway though, so even if the terrorists were u…
Sorry for the delay in responding, I gave up yesterday because there was no option to reply even after a very long time.