In the first place Pilate was already influenced by the warning of his wife about Jesus being a righteous man and not to be part of the excecution of jesus. But I think that what determine most the reluctance of Pilate to excecute Jesus was the conversation that was hold between Pilate and Jesus. It was until he heard Jesus that he could perceive that the charges against jesus were not worthy to execute him, and also because through the answers of Jesus he could perceived sincerety, transparecy, power, humbleness and holyness in his behaviour and words, and consecuentely, was convinced that Jesus was not a really threat to Roman's rule as the Priest said. And probably he recognized a sense of truth in Jesus' words. Probably he recognized him as a King, not of earth but of heaven.