How did three sons Shem Ham Japheth having the same mother and father Noah develop into three distinct family groups or races over such a very short period of history?

This is The Bible. Time is not specifically measurable. These were nomadic peoples who traveled to different regions. Typically, they would intermarry with the local peoples once they were settled. There is, however, no written history as to exactly what did happen. At some point you have to take the information on faith and go from there.