It is said that our intuition tells us we have free will.
What is intuition? It is said to be the way we know things though we cannot understand how or why we say we know them. It is like the way you know you can talk though you do not exhaustively know how you can do so. This would make it a rational belief even though we have no evidence or proof.
Surely it is better to have evidence and rational justification for saying that free will is probably real. If you want evidence your free will does not respect you if it does not give it to you. If you want evidence and your free will belief has little or no justification then your free will is not really free will.
Intuition is a sense but a very unreliable one.
It is not our intuition that is telling us that we have free will at all. We simply feel free and that is why we think we are free or have free will.
Some argue that if reason says free will is impossible, experience says different. They say, "Experience says free will is real even if it is a miracle. We must listen to experience for reason cannot explain all things anyway". But reason matters more than experience. If reason says there is no pink angel making your breakfast and you see the angel doing just that then you will just have to remember that you can hallucinate and maybe that is what is happening.