If you take two random variables $p,n$ distributed like zero-truncated normal distributions (ie: normal distributions with their negative-number tails clipped off) and you take the ratio $p/(p+n) = 1/(1+n/p)$ you get this pretty cool distribution whose PDF looks like the attached picture. It's valid on the domain [0,1] and one interpretation of it is the ratio of some positive values $p$ to a total value $T = p+n$, when the constituent values $p,n$ are uncertain