When it's a draw and there has been previous characters who has held prestige, the draw is settled like so:
In the case of a draw, the Hero who has held the leading Prestige for the longest is selected as the Prestige Leader.
This means, that if Rabbit held the prestige for one round and Wolf then drew prestige the next round, Rabbit would maintain prestige leader until they either lose prestige to a level beneath someone else, or someone overtakes them in prestige.
This can behave a bit oddly where sometimes a flip can happen. If you lose a prestige and then gain one in the same action, it means someone who was drawing with you will take the lead as you had a momentary loss of prestige, so dropped to 2nd place and then gained another prestige back to joint first. Since you've now held the prestige the least amount of time, your character is put in 2nd place.
I can't remember what happens when there is a draw and there is no previous prestige, I need to double check that. I think no-one is given it and instead the king decides which decree to enact