Creative and logical analysis of an interesting murder case

Jason, John and Peter are about trying to across a desert. In order to prepare for such challenge, Jason fills a extremely large bottle of water. John puts deadly poison into the water while Jason is unaware. Peter, on the other hand, goes 50 miles out into the desert to wait for Jason, then dumps out the water in the bottle. (Neither Jason nor Peter knows at that point that the water is poisoned.) Peter and John, who have separate supplies of water, return home safely. Jason dies of thirst in the desert.

John and Peter are brought to court after the event is exposed to public. John says, Jason did not die of poisoning. It was not I who killed him. Peter says, What I did lengthened, not shortened, Jason’s life. Do not blame me.

Who killed Jason? Please don’t say John and Peter are both guilty and responsible for Jason’s death. That much is obvious, and easy to answer. If you were the judge at the court, who would you say is guilty of the actual murder? Give your reasoning.