Actually the predestination of the betrayal is very clear in scripture. Satan did not just "posses" him. Satan was placed IN him
Jhn 13:2 And supper being ended, the devil having now put into the heart of Judas Iscariot, Simon's [son], to betray him;
The plan from before the foundation of the earth
This doesn't say that Satan was placed in him. It says that the devil put the thought/desire in Judas's heart to betray Jesus.