Wiktionary
adv. confidentially, privately, off the record.
Wikipedia
In Confidence is a British television series presented by Laurie Taylor and executive produced by Victor Lewis-Smith, in which a one-on-one in depth interview with a public figure takes place over the course of about an hour. The object of the interview is to try to determine who the subject really is and how they think. The show airs on Sky Arts in the UK.
Usage examples of "in confidence".
This kind of talk, even in confidence, soon got Washington into trouble.
One thing she knew: the crimes were becoming more violent as the attacker grew in confidence.
You seem awfully sympathetic, and I don't mind telling you in confidence that I simply worship the ground that girl walks on.
And I realize it was unfair of me to try to get you to tell me things told you in confidence by a friend.