This is blue-sky hypothesising. As far as I can tell, none of these "low enough" "finite probabilities" have ever been estimated; neither is it clear that one could do so.
Exactly. So for practical operation of the aircraft, we ignore them.
If you wish to make it compulsory, you devise a provably-correct algorithm, prove it correct, and put the proof in the public domain for peer review.
That doesn't solve your problem. You need a provably correct
implementation of the algorithm. Have the manufacturers "open-sourced" their code yet?
And if you can't do that, you let it be advisory and let people choose what to do. And respect them for making a choice which, while different from yours, is still rational.
The Tu-154 crew chose, or should I say "elected" to do something different. People died. I'm not saying they didn't have reason (their SOPs seem to have been at odds to everyone else's, for one thing) but the end result was disaster. An avoidable disaster, one that TCAS was invented to prevent. You can "choose" to drive on the opposite side of the road to other people but I don't think you'll get much respect for it.
You don't "know" that; in particular, you don't know about that 99.99%
That leaves us in a bit of a stalemate as you don't "know" either... That gives me a (miniscule) chance of being absolutely correct with my random typing of decimal places.
Point is, we, the airline industry, have been given a collision avoidance tool that has been approved and accepted, even mandated, by many national aviation authorities. For effectiveness it relies on timely responses to given commands, so it loses much of its appeal if these commands are ignored or flown against. Thus the need for legislation.
As a pilot I'm paid to consider possibilities... The FAA, CAA, LBA, etc. could be making a huge mistake and exposing us all to increased risk from this system and I shouldn't trust it... But where is the evidence? Well, it's all proprietary stuff so looks like it'll be some time (if ever) before any non-affiliate can come up with any data one way or the other. So I'll just have to go on the information available which seems to be: it does what it says on the tin and you'd be foolish to ignore it.