Did Jesus explicitly confirm Judas as his betrayer at the Last Supper, and if so, why did the disciples not react?

Mark 14:20 >And he said unto them, [It is] one of the twelve, he that dippeth with me in the dish. Luke 22:21 >But behold, the hand of him that betrayeth me is with me on the table. He doesn't single Judas out at all here. Matthew 26:25 >And Judas, who betrayed him, answered and said, Is it I, Rabbi? He saith unto him, Thou hast said. Plenty of others asked in turn if they would be the one, and when Judas asks, Jesus seems to reply affirmatively. Did he do so quietly? Was no one else paying attention? John 13:26 >Jesus therefore answereth, He it is, for whom I shall dip the sop, and give it him. So when he had dipped the sop, he taketh and giveth it to Judas, [the son] of Simon Iscariot. Again, why wasn't this noticed or remarked upon, or acted upon by anyone? Did they not believe what he was telling them? Did they not find Judas' subsequent hasty departure suspicious? John extends the incident a bit further: John 13:27-30 >And after the sop, then entered Satan into him. Jesus therefore saith unto him, What thou doest, do quickly. **Now no man at the table knew for what intent he spake this unto him.** For some thought, because Judas had the bag, that Jesus said unto him, Buy what things we have need of for the feast; or, that he should give something to the poor. He then having received the sop went out straightway: and it was night. [bold mine] How could they not have known, when he straight out told them what was going to happen and who was going to do it? How could any of them think "Hey the guy that Jesus just said is going to betray him is probably just running off to the shops to get some more food, probably for the poor."