Hamlet does not kill Claudius when he assumes that he is praying because he doesn't want Claudius to have the luxury of going to heaven while his father, unjustly murdered, suffers in hell. ... He doesn't want to do Claudius the "favor" of sending him to heaven.

Why does Hamlet choose not to kill Claudius?

Hamlet delays killing Claudius because Claudius represents Hamlet's innermost desires to sleep with his mother Gertrude. ... Hamlet may believe he is delaying from fear of sending Claudius to a “heavenly” afterlife; however, there are times when Hamlet could have killed Claudius when he was not at prayer.

Why doesn't Hamlet kill Claudius when he is on his way to meet his mother and has the opportunity to?

Hamlet therefore chooses not to kill Claudius because he wants Claudius to suffer for his sins and actions during his life, rather than merely kill him and give him a ticket straight to heaven. He does not want to kill Claudius when "he is fit and season'd for his passage" as he says in the same scene.