Im confused can you help me

A king has three sons and he wants to split his kingdom equally among them, so each of them gets 1/4 of the kingdom but to the smartest he wanted to give the remaining 1/4. So he summoned all his sons into one room and blindfolded them and put a dot of white paint on each of their heads. Then he told them to take of their blindfolds off and to knock three times if they saw white so they all knocked. He then said that whenever they figured out what color they had on their head and could tell him how they knew then they would get the remaining 1/4 of his kingdom. After a while one of the boys got up and told his father that he knew that he knew that he had white paint on his head and his father asked how he knew and the son told the father that he was a fair father and wouldn't give his brother both white paint and give him black and the father said he was an idiot and told him to go back and sit down. After little while longer another boy got up and told his father that he knew what color he had on his head and could prove it. How could he?