[eru]

Usually 'this sort of thing' would go to the extremes: colours that are already prevalent have a bigger chance of getting more added to them.

It's interesting that they don't.

Normal distribution would be extremely weird and unexpected (and not even really possible): we know for sure that the proportion in the end has to be between 0% to 100%. Normal distributions don't have such cutoffs.

[kgwgk]

On a log-odds (logistic) scale, though, we get something that resembles a normal (a logistic distribution).

[eru]

Yes, a uniform distribution in the space of probabilities between (0,1) would give you something bell-curve shaped in the log-odds scale.

The log-odds scale also makes it clear why probabilities 0 and 1 are very special: they only show up as limits in the log-odds scale.