He is given, so the record tells us, an evil spirit from God. Sometimes in the KJV the word ‘spirit’ is spelt with a small ‘s’, and sometimes, where the word ‘evil’ isn't employed, it is given a capital ‘S’.
In a sense every one of us has a bad inclination in some respect, many of them. We have fallen hearts. We walk with the Lord, and that old nature is under restraint unless we let it out. But in this case Saul is a rejected man. He has no help from God, and this evil disposition has liberty, because he has authority, and because God's restraint is taken from him. If you or I are in a sad frame of mind, and there are thoughts going through our head that drag us down – perhaps we are grieved about something or other, or deeply disappointed, or we have been hurt and wrong thoughts arise in us, resentful and antagonistic thoughts – none of these things take away our responsibility. We are responsible for bringing those thoughts to heal. Even if we are in a phase of sadness or depression, we don't have to just hang onto those thoughts, and get on the treadmill, and let them go round and round in our head. We have a responsibility to try to take them in hand, to pray to God, to worship him, to switch our thoughts to better and more wholesome things, particularly if those thoughts are intentions to hurt or retaliate against somebody or sin in some way. But of course Saul isn't a believer, and he doesn't attempt to process his thoughts or to contain them. He allows them to escalate into thoughts of outright murder. It didn't take long, and he was attempting to kill David.
We see how jealousy can not only inflame anger, but it can make us imagine things that are not true; it can make us badly misjudge others. Envy creates suspicion, and suspicion attributes all sorts of ugly motives to others which are not really there. Thus envy feeds on itself. The truth is that David feared the Lord and was scrupulously careful not to do anything against Saul, whom he regarded as the Lord’s anointed. It was not David who was against Saul, but it was the Lord. And the Lord would elevate David to the position of king and replace Saul without any help from David himself.