What is the theoretical probability of randomly selecting a 3 child family with 3 girls?

The gender of children is not a constant. It depends on the parental predispositions - mainly on the father's genes but apparently the mother's age can also affect the gender. The details of these influences are not understood well enough to develop an accurate model.

If you make the simplistic but unjustified assumption that both genders are equally likely, the answer is 1/8.