My players want to fight the BullyWug king

After meeting the king and going towards the Soggy Court, they came across the fighting ring. They are being accompanied by a tour guide-esque character who told them that it is how new monarchs are chosen (fight to the death). And one player has the idea to challenge the current king to a battle in order to try to become the new king. So far, I’ve not seen any reference in the book as to what to do in this situation. I don’t know if I should have them be thrown in prison and stage a prison escape or let it play out, as I’ll need to figure out what happens with Bavlorna as well.

Any advice on how to proceed? Anything is appreciated