How could Judas not believe?

This question just came in, and it's a good one. 

"How could Judas Iscariot, a first hand observer, have discredited all he saw. I feel like seeing first hand miricles and healings and teachings would have convinced me. Shouldn’t Jesus have been able to convince even the most doubtful? I guess in a way he did because he killed himself and must have been out of guilt. I’m not sure what the ultimate question is here."

This is a really great question because it deals with a false notion. I've been told by a number of atheists that, "if God would simply reveal himself, they would believe."

Although this sounds reasonable, Jesus disagrees. 

Jesus told a story recorded in Luke 16:19-31. It's usually called Lazarus and the Rich man. In it Jesus tells of a rich man who refused to believe during his life. While in Hades, the rich man looks up and sees Lazarus and Abraham in paradise. Jesus relays a conversation between the two. The rich man begs Abraham for help. He says,

"Father Abraham, have pity on me and send Lazarus to dip the tip of his finger in water and cool my tongue, because I am in agony in this fire."

Abraham explains that it's impossible. The rich man makes a second request. 

"Then I beg you, father, send Lazarus to my family, for I have five brothers. Let him warn them, so that they will not also come to this place of torment."
“Abraham replied, ‘They have Moses and the Prophets; let them listen to them."
“No, father Abraham,’ he said, ‘but if someone from the dead goes to them, they will repent."
“He said to him, ‘If they do not listen to Moses and the Prophets, they will not be convinced even if someone rises from the dead.”
So we learn a really difficult lesson in this story. It's a lesson that I actually find hard to believe. Though I feel like I've seen it in action. Through this story Jesus claims that even if someone rises from the dead there are many that will not be convinced. 
Jesus uses this to teach the exact answer to the question asked on this post. Judas spent all this time with Jesus, he saw the miracles, he witnessed the power of God. However, he was still a crook. 
John 12:6 says, "he was a thief; as keeper of the money bag, he used to help himself to what was put into it."
Just because Judas was a thief doesn't mean that Judas didn't believe in Jesus. Even as believers, we can do terrible things. Is it possible that Judas believed, even though he was evil?
Jesus said in John 6:64, "Yet there are some of you who do not believe." For Jesus had known from the beginning which of them did not believe and who would betray him."
It's pretty clear here that Judas never believed in Jesus. He may have believed parts of the message. I think he probably believed that Jesus could be a political ruler. I think that Judas might have thought Jesus would defend himself when the mob arrived. Some people think that Judas was trying to force Jesus' hand. Some think that Judas was trying to usher in Jesus as King. Judas' commitment to Jesus was self centered but apparently he never believed in him for eternal life. 
So how is that possible? How could Judas spend three years with him and still not believe?
The premise that "all the atheist needs is evidence" is faulty. It's faulty because it implies that there is, as of yet, no evidence given. 
The presence of Jesus in the world is the evidence of God's existence. The resurrection of Christ is the evidence of God's existence. The miracles the performed is the evidence of God's existence. 
I'm convinced that most of the excuses given for disbelief in Jesus are not for lack of evidence but for lack of receptiveness. Judas was not the only who with this kind of response. Here's another great example of this. 
After Jesus had risen from the dead, and many witnesses had looked at and touched him, Jesus told his disciples to meet him on the Mount of Olives. When they arrived there, Jesus appeared to them, right before he ascended into the sky it says this. 
"When they saw him, they worshiped him; but some doubted."
After all they had seen, some still doubted. Now that doesn't mean they weren't believers. Those who doubted probably believed in him and had eternal life. However, they felt doubt.
This is huge. It further illustrates that seeing MORE evidence doesn't necessarily produce more faith. In Judas' case, he had as much evidence as anyone could ever want and still didn't believe. He had more evidence than we will ever have (except in the life to come.) It's possible to see miracles and still not believe. 
I think at this point, it would be important to remember what the believe means. 
Believe = Convinced / confident that something is true. 
What do we need to be convinced of in order to gain eternal life? We need to believe that Jesus is the giver of eternal life, and freely gives it to anyone who believe in him for it. 
Scripture teaches us that Judas never did this.