The reference to the Passover here is not referring to the Passover supper, which had been eaten the night before (shortly before they arrested Jesus). Rather, it refers to the Feast of Unleavened Bread which immediately followed for seven days (cf. Matt. 26:17).
"Pilate then went out to them and said, 'What accusation do you bring against this Man?'" (John 18:29). Pilate, being familiar with their customs, came out to them and got straight to the point.
"If He were not an evildoer, we would not have delivered Him up to you" (John 18:30). The Jewish religious leaders attempt to get Pilate to accept their verdict blindly and condemn Jesus without one shred of evidence being presented (or more accurately, fabricated). This approach emphasizes the weakness of their case, for they want Pilate to assume that Jesus is a wicked man simply because they declare him to be such!
"You take Him and judge Him according to your law" - Pilate, though not a godly man, at least had a sense of justice. He would not automatically condemn a man on the request of others (or at least not at the request of the Jews). He declares that they should judge Jesus according to their law, perhaps assuming that they have not done so yet since they did not formally state any specific charges against Jesus a moment earlier.
"It is not lawful for us to put anyone to death" (John 18:31). The Jews plainly declare their intent here. They desire Jesus to be executed, yet they still haven't told Pilate a good reason why. Under the Jewish law, it was lawful to execute those who commit certain sins. However, when the Romans subjugated the Jews in A.D. 6, they took away their right of administering capital punishment. This fact is the only reason why Jesus was still alive at that moment. The Jews would have killed him hours ago had they not feared Rome's response for doing such without permission.
"That the saying of Jesus might be fulfilled which He spoke, signifying by what death He would die" (John 18:32). Had the Jews been able to execute Jesus on their own, He would have certainly been stoned for His "blasphemy" (e.g., I Kings 21:13). However, Jesus knew and foretold (cf. Matt. 20:18,19; John 12:32-34) that He would be crucified. Crucifixion was the current Roman method of capital punishment.
The Jewish leaders now begin to bring false accusations against Jesus - "We found this fellow perverting the nation, and forbidding to pay taxes to Caesar, saying that He Himself is Christ, a King" (Luke 23:2). The first charge, regarding "perverting the nation," was ambiguous and not true whatsoever. The second charge was an outright lie for Jesus had never discouraged (and definitely not forbidden) anyone from paying taxes (e.g., Matt. 22:21). The third charge had an element of truth to it. Jesus was a spiritual King, but such was not offensive to the Roman government. This charge, in conjunction with the other two, is presented in a manner that attempts to portray Jesus as a political king, and thus a threat to Rome. Of course, Jesus had several opportunities where He could have easily claimed political power as a Jewish leader, but that was not His mission and He always refused to do such (e.g., John 6:15). Jesus was no threat to the Roman government.
We will consider Pilate's examination of Jesus in our next lesson.