"Favorite Betrayal" probability in IRV (alternative probabilistic model)

As requested I have redone the calculation
that was here
but now assuming S,T,U,V,W,X,Y,Z are no longer normally distributed
but rather are the lengths of the
intervals separating sorted random uniform variables in [0,1].
This also is known as the Dirichlet model.

Under this new probabilistic model:
Instead of 19.6%, my Monte Carlo program finds
as the probability P of a favorite betrayal scenario in a 3-canddt IRV election:
P = 20.2%.