Your Prince and you found the assassin before everyone else did. You have him jailed but not executed and while you could just leave him there while everyone else investigates people there is a faster way…
Day X:
“ATTENTION UNSEEN! THIS IS THE PRINCE! Your assassin is being held Hostage. I am willing to dispose of him rather than keep him in pain on ONE CONDITION!! It is my understanding that you have one of our own in your possession. Hand him/her over and your assassin shall be freed. You have 1 night to think about this. Choose wisely.”