We know that belief is important, but we can also see by the following verse that belief by itself is not sufficient:
Ja 2:19 Thou believest that there is one God; thou doest well: the devils also believe, and tremble.
The devils believe there is one God; indeed, they were once in heaven with God. They saw him. They spoke to him, and he listened to them. The devils are fallen angels -- angels who followed Lucifer in rebelling against God. The rebellion failed, and Lucifer, together with one third of the angels -- those that followed him -- we cast out of heaven.
Is 14:12 How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations!
13 For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north:
14 I will ascend above the heights of the clouds; I will be like the most High.
15 Yet thou shalt be brought down to hell, to the sides of the pit.
They are condemned to ultimate death in the lake of fire:
Re 20:10 And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.
So the devil believes, but he has no hope. Many of the promises of God are blessings. Still others are curses. Many of these promises are unconditional, but some of them are conditional: God says, ``If you do that, then I will do this.''
But the above verse is prophetic, being written in the future perfect tense. It is an event that occurs in the future, but it is being viewed form a point even farther into the future, and from that vantage point, it is spoken of as being in the past. It is already a done deal. There is no conditional aspect about it. It is history. The devil and his imps are doomed. They have no escape. They have no hope.
So, even though Satan believes in God, he has no hope. Satan lacks an necessary ingredient for faith: hope. Belief is necessary, but not sufficient. Hope is also necessary, but likewise not sufficient.