The characters in question had a score of 7 (intellect or piety).

My understanding is that it is 3.33% per point (chance is your score / 30), so this would give it a 23% chance. But I got this result twice in about 40 tries. That's 5%. Admittedly not a huge sample size so that might be it, but it feels like a significant variance.

It does make things easier for characters that want to switch though.