high confidence

Please give some context.

In american usage, you have high confidence in something, intended to imply that you're very confident about it. As far as secrecy, we would use confidential, classified or top secret.

high confidence = very confident = very certain that ...
Pressure works ("high confidence")

This week's national intelligence assessment says with "high confidence" that although Iran was indeed working on a bomb until the autumn of 2003 it then stopped. By the middle of this year it had probably ("moderate confidence") not started again. And unless it got fuel for a bomb from abroad it would take at least until late 2009 ("moderate confidence") but more likely between 2010 and 2015 to make it at home.

So, probably, ihe phrases mean, very confident (very certain) ...?

The national intelligence assessment (whatever or whomever this is) is rating its own statements for accuracy. So if it makes a statement with "high confidence," it is saying that it speaks with utmost accuracy.