The premise of your question is wrong. The warrior class and elite class were usually the same people (warrior-aristocrats), so the third class was usually made up of peasants, who made up the vast majority of the population (that is, at least 80% and sometimes more).
The Roman patricians and equites, Korean yangban, Japanese kuge or kazoku and samurai, European knights and noblemen, and Hindu Kshatriya were all part of the warrior-aristocrat class of their societies. One of the few exceptions to this was China where they had a scholar-bureaucrat class that effectively replaced the warrior-aristocrat class much earlier.
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