I do not believe that Jesus believed in Satan. I believe that when Jesus referred to Satan it was figurative, and he was referring to the lower selfish nature of man, the evil ego within, not an evil entity outside. For example:
Matthew 16:23-26 But he turned, and said unto Peter, Get thee behind me, Satan: thou art an offence unto me: for thou savourest not the things that be of God, but those that be of men. Then said Jesus unto his disciples, If any man will come after me, let him deny himself, and take up his cross, and follow me. For whosoever will save his life shall lose it: and whosoever will lose his life for my sake shall find it. For what is a man profited, if he shall gain the whole world, and lose his own soul? or what shall a man give in exchange for his soul?
When Jesus said said unto Peter
"Get thee behind me, Satan: thou art an offence unto me: for thou savourest not the things that be of God, but those that be of men" Jesus was referring to worldly things that are not of God, things of the flesh.
In those verses, Jesus was saying to deny our selfish desires, things we want that are not of God, and to follow in Jesus’ Way. For whoever will live for self and the world shall lose his eternal life, but whoever will sacrifice his life for the sake of Jesus shall gain eternal life.
of man. In Matthew 16:23 Jesus was taking to His lower material nature which He was struggling to ward off. Jesus was not talking to an evil entity called Satan.
That is a modern reading, changing the meaning. In the religion Jesus believed in the devil.
Jesus exorcized demons out of pigs as well. He believed the demonology of the day. In the story they are real. But it's a story and like revelations are not actually true. No matter who makes the claim.
David Hume -
Which is more likely - that a man should be used as a transmitter by God to deliver some already existing revelations, or that he should utter some already existing revelations and believe himself to be, or claim to be ordered by God to do so?
What Jesus Said About Satan
Jesus said a good deal about Satan.
He called him:
"the enemy", Matthew 13:39.
"The evil one", Matthew 13:38
"The prince of this world", John 12:31; 14:30
"A liar", and "the father of lies", John 8:44.
"A murderer", John 8:44.
He said that he "saw him fallen from heaven", Luke 10:18.
That he has a "kingdom", Matthew 12:26.
That "evil men are his sons", Matthew 13:38.
That he "sowed tares among the wheat", Matthew 13:38,39.
He "snatches Word from hearers", Matthew 13:19; Mark 4:15; Luke 8:12.
The he "bound a woman for 18 years", Luke 13:16.
That he "desired to have Peter", Luke 22:31.
That the has "angels", Matthew 25:41.
That "eternal fire is prepared for him", Matthew 25:41
The Bible represents Satan as:
"The tempter", Matthew 4:3
"The prince of demons", Matthew 12:24; Mark 3:22; Luke 11:15.
"Source of demoniacal possession", Matthew 12:22-29; Luke 11:14-23
That he put the betrayal into the heart of Judas, Jn 13:2,27.
That he perverts the Scripture, Matthew 4:4; Luke 4: 10,11
That he is "the god of this world", 11 Cor. 4:4.
That he is "the prince of the power of the air", Ephesians 2:2
That he "fashions himself into an angel of light", 11 Cor. 11:14.
That he is our "adversary", 1 Peter 5:8.
He is "the deceiver of the whole world", Rev. 12:9; 20: 3,8,10.
Calls him "the great dragon", "the old serpent", Revelation 12:9; 20:2.
The "seducer of Adam and Eve", Genesis 3:1-20.
That he will "flee if resisted", James 4:7.
That he caused "Paul's thorn in the flesh", 11 Cor. 12:7.
Hindered Paul's missionary plans, 1 Thess. 2:18.
Caused Ananias to lie, Acts 5:3.
That Gentiles are under his power, Acts 26:18.
That he blinds the minds of unbelievers, 11 Cor. 4:4.
False teachers are "a synagog of Satan", Rev. 2:9; 3:9.
Can produce false miracles, 11 Thes. 2:9.
Is the moving spirit of the ''Apostasy'', 11 Thes. 2:9
As a roaring lion seeks to devour Christians, 1 Peter 5:8
Is overcome by faith, 1 Peter 5:9.
Is wiley, Ephesians 6:11.
Is the spirit that works in the disobedient, Ephesians 2:2
Moved David to sin, I Chron. 21:1.
Caused Job's troubles, Job 1:7-2:10.
Was the Adversary of Joshua, Zech. 3:1-9.
Gets the advantage of Christians, 11 Cor. 2:11.
Evil men are his children, 1 John 3:8,10.
Is there really a devil? The language of Jesus certainly indicates his own belief in the existence of a personal devil. Jesus knew what He was talking about. If Jesus was merely accommodating himself to popular error, His words are no revelation of truth at all, for who, then, can discern between the actual truth that He is aiming to teach and the error that He speaks of as if it were truth?
(Halley's Bible Handbook pg.400)