Advice on DMing deception/insight checks

Hey, I DM for a group of friends. We're in a campaign setting where they're meant to be the heroes. To be fair, their characters fit the role well and are invested in their characters after 3 years of play. Yesterday, ,one of my players killed an innocent civilian. This is the first time that this character have done this, and the character is currently experiencing varying emotions for doing this.

However, I want to know how can I DM the roleplay scene because I am having difficulty figuring out the power of deception rolls etc.

If the King accuses them of doing the crime, can they roll deception against the King's insight? If they succeed in their deception roll, what happens?