Rambam, The Laws of Kings and Wars, 3:8 (Chabad.org)
Anyone who rebels against a king of Israel may be executed by the king…
Shaul was considered righteous since he believed he was putting down a rebellion.
The king may only execute people by decapitation. ……However, he may not confiscate property. If he does, it is considered theft.
This is why Achav couldn't just take the property.
Rambam ibid. 4:9 (Chabad.org):
The property of all those executed by the king, belongs to the king. Similarly, all the treasures belonging to the kings of the kingdoms which he conquers become the property of the king.
So Achav (or Izevel) thought that by scheming to have Navos framed and killed, they could legally take his property. However, G-d was not fooled, and he punished Achav and Izevel for their evil.
Side note: Achav may not have been considered a king at all, halachicly.
Rambam ibid. 1:8 (Chabad.org)
If a prophet appoints a king from any other tribe of Israel and that king follows the path of Torah and mitzvot and fights the wars of God, he is considered as a king, and all the commandments associated with the monarchy apply to him.