It may seem strange that having secured a confession from Jesus that He was the King of the Jews Pilate would declare Him innocent. The answer is that Luke did not record the conversation that took place between Luke 23:3-4 (cf. John 18:35-38). In this conversation Pilate learned that Jesus did not claim to be a king in the ordinary sense. He concluded that Jesus posed no treat to the political stability of Roman interests in Palestine. Only Luke recorded Pilate"s official verdict that he gave to the Sanhedrin (cf. John 18:38; John 19:4; John 19:6). Perhaps Luke chose not to record what John did because for his readers the claim to be King of the Jews was ludicrous; it would have been obvious to Greeks that Jesus posed no threat to Rome. [source][source][source]
In Acts as well as in Luke our writer recorded the innocent verdicts of government officials when passing judgment on Christian leaders (e.g, Acts 18:12-17; Acts 19:35-41; Acts 25:23-27; Acts 26:30-32). He obviously wanted to assure his readers that Christianity was not seeking to overthrow the Roman Empire and was not hostile to Roman civil authority. [source][source][source]