Here's the scripture for that that I know....
YLT
Joh 16:7 `But I tell you the truth; it is better for you that I go away, for if I may not go away, the Comforter will not come unto you, and if I go on, I will send Him unto you;
Joh 16:8 and having come, He will convict the world concerning sin, and concerning righteousness, and concerning judgment;
Joh 16:9 concerning sin indeed, because they do not believe in me;
Joh 16:10 and concerning righteousness, because unto my Father I go away, and no more do ye behold me;
Joh 16:11 and concerning judgment, because the ruler of this world hath been judged.
When we didn't believe and were in the world, we were convicted of sin, not believing in the Savior, and are lead to repentance because of the righteousness of the Christ which we see in Him by His work on the cross, etc. We can know that Satan has already been judged and without Christ we would be in the same boat.
I do agree with Willie about how and what we as believers are convicted of. Christ is righteous and we are made righteous in Him. Our behaviors should be a reflection of Him and of our position in Him.