I think in some sense, all three were fundamentally "rebels" in their character and it was partly this that drove them to capture powerful states so that they could rule them as they wished. Being something of outsiders in terms of origin[1] probably helped stirr up feelings of being outside the mainstream, encouraging rebelliousness and spurring them to the extremes of personal commitment needed to fulfill their ambitions.

[1]I suspect they were also "outsiders" in terms of social class - they were not born into the classes that typically ruled their countries.