Jesus explains to the Pharisees why they should believe in him. He begins by saying “If I testify on my own behalf, my testimony is not true.” This cannot of course be taken in the sense that Jesus would lie about himself. Jesus does not ever say, “I am the Christ”, because he does not need to. Peter says it, and then Jesus confirms it. When he is asked whether he is the Christ at his trial, he says, “You say that I am.” In other words, only the Christ would be accused of being the Christ without ever having said it. Where did the idea come from? Jesus was not raising an army. He never fought a battle. He never called himself the Christ.
Jesus says that John the Baptist witnessed to him. The Pharisees thought that John the Baptist was an impressive prophet, since he fit the idea in their minds better. He fasted and lived in the desert and was killed by the king. It must have seemed very strange to the Pharisees that this great and holy man testified that Jesus was the Christ. Jesus is reminding them of this contradiction: they all thought that John was a prophet, but they did not believe his greatest prophecy.
Also, the Pharisees could see that Jesus never sinned; they could see the healing and other miracles; they could see the sinners repenting and following Jesus. If I told you that I was the Messiah, you would all laugh, since I am not that impressive, and if I did not tell you, it would never enter your mind that I was. When Jesus says that his works are one of the witnesses, he does not just mean his miracles, but everything he ever did. People could see that he was not like them. Today we see the works of Jesus in his saints; we see sinners live extraordinary lives. We know that someone greater must be at work.
The third witness is the Father. St. Peter did not know Jesus was the Christ because he figured it out, but because the Father revealed it to him. Faith is strongest when there are no reasons behind it, when we simply believe. There are times when we are so filled with the love of God that, without being able to explain why, we just laugh at the idea that there is no God.