Hobbes believed in an absolute monarchy exactly because people are driven by greed and ambition. They need to give complete power to the sovereign so that they will not destroy one another through their greed and ambition.
This is not to say that the sovereign was perfect or without greed. But the sovereign was just one person. Therefore, the sovereign would not have to be in conflict with anyone else. There would be no "war of each against all." Instead, the sovereign would be pursuing his own self-interest. In doing so, he would do things that would generally help his country. Some individuals might at times be hurt, but the overall good of the people would be served.
The main point, then, is that the sovereign is one person and will not tear the society apart by pursuing his greed and ambition. If, on the other hand, everyone is acting on greed and ambition, society is torn apart.