The Spirit convinces the world of righteousness in two respects. The first is that only He can show men that their righteousness is worthless unless it is dependent upon the righteousness of Christ and His atoning work on the cross, which was one of the goals of the Messiah (Dan 9:24). The Holy Spirit certainly has His work cut out in this respect (Rom 10:3).

Daniel 9:24  “Seventy ‘sevens’ are decreed for your people and your holy city to finish transgression, to put an end to sin, to atone for wickedness, to bring in everlasting righteousness, to seal up vision and prophecy and to anoint the most holy.

Romans 10:3  Since they did not know the righteousness that comes from God and sought to establish their own, they did not submit to God’s righteousness.

Secondly, the Spirit is going to convict or convince the world of the righteousness of Jesus Christ (1 John 2:1, Luk 23:47). Barclay observes, “When you think of it, it is an amazing thing that men should put their trust for all eternity in a crucified Jewish criminal. What convinces men that this crucified Jew is the Son of God? That is the work of the Holy Spirit. It is the Holy Spirit who convinces men of the sheer righteousness of Christ.” Though His enemies had put a label of criminal on Him, the Spirit justifies Christ as being righteous (1 Tim 3:16).

1 John 2:1  My dear children, I write this to you so that you will not sin. But if anybody does sin, we have one who speaks to the Father in our defence—Jesus Christ, the Righteous One.

Luke 23:47  The centurion, seeing what had happened, praised God and said, “Surely this was a righteous man.”

1 Timothy 3:16  Beyond all question, the mystery of godliness is great: He appeared in a body, was vindicated by the Spirit, was seen by angels, was preached among the nations, was believed on in the world, was taken up in glory.

The Holy Spirit could not convince the world of the righteousness of Christ until after the death and resurrection of Jesus. To explain why, Barrett notes that “Jesus’ death proved his complete obedience to the will of God, and his exaltation proved that his righteousness was approved by more than human acclamation.” If Jesus had remained dead and in the grave that would have shown that He had His limitations and faults just like the rest of us, but His miraculous resurrection proves that God interevened on Christ’s behalf and thus guaranteed and proved that Jesus truly was completely and perfectly righteous.

His resurrection and ascension also hold great promise for our own righteousness. We already know that everyone is a sinner and is totally incapable of living a righteous life (Rom 3:23), so if Christ lived a perfect life as an example for us and then didn’t do anything to help us do the same, we would be more frustrated and worse off than we were before He came. However, His resurrection and ascension prove to us that we will follow His example of living a righteous life, because He now sits at the right hand of the Father to help us do so (Rom 8:34).

Romans 3:23  for all have sinned and fall short of the glory of God,

Romans 8:34  Who is he that condemns? Christ Jesus, who died—more than that, who was raised to life—is at the right hand of God and is also interceding for us.