At the Last Supper, it was obvious that Jesus already knew what Judas was going to do (Jn. 13.18-30). We at least know that he told John and Peter that this was to fulfill the Scriptures. Peter reflects that understanding in Acts 1.16. It wouldn't surprise me at all that in one of Jesus's discussions with the disciples after the resurrection that this conversation came up. The disciples had the understanding that Jesus was omniscient (Jn. 16.30; 21.17).

John 6:64 ... But Jesus knew from the beginning who they were that believed not, and who should betray him. How could you know that Jesus knew from the beginning?

As the Bible was not written by Jesus himself I ask myself how did the writer knew that Jesus knew from the beginning in fact that there’ll be a betrayal and who will betray him?