Betrayal. If the eldest prince betrayed the kingdom with all his guards in charge of the security, killing whoever he wants wouldn't be difficult. Moreover, although the king was still far stronger than the eldest prince who had just reached the Rank 9, the king wouldn't be on guard in front of him, so the chances of the king being defeated by and sneak attack or a trap were high.
Yale had no proof for that guess, but it was very difficult that the capital reached the state Yale had seen in the vision without that kind of situation. In any case, there was nothing to lose for tracking Sebe and be aware of any sneak attack towards him; if Yale's guess were wrong, they would have just lost a day.