There are 188 rare champions in total, and 14 factions. Each faction has roughly three rare void champions, so that leaves approximately 146 rare champions summonable from ancient shards. Of that set, 18 are undead hordes. UH also happens to have the most rare champions of any faction.

Quick back-of-the-envelope math suggests that your chance of getting a rare UH champion from ancients is therefore roughly (18-3)/146 = 10.2%.

This isn't exact, of course, since I'm ignoring the possibility of that ancient resulting in an epic or legendary, but it should be close enough.

okay ty so much!