Right! That does half answer my request :) Those crazy infinities,right? :)

The other half is where I said "reasonable", like the three approaches from the article are--in my subjective opinion--quite reasonable. Picking samples from an uncountable (right?) infinity of options explicitly to satisfy the desired probability, somewhat less subjectively, is not :)

So yes, your method allows for B arbitrarily close to 0 or 1 (or anywhere in between), and it's clever.

But let's not go for "arbitrarily close", but just "very close", or "closer". I wonder if there's (subjectively) reasonable ways of sampling chords from a circle, like you could explain with a realistic(ish) scenario for a ninja pizza slicerator or an erratic mermaid, that give a probability even less than 1/4th or more than a half?