Formula for the ambient light intensity of a scene?
Using an 'ambient light' term in your lighting calculations is an approximation of the indirect light reflected around the scene. Usually it's up to the artist to choose an appropriate value. There isn't really a formula, because the indirect light is dependent on many factors:


Light intensity
Light shape
The BRDFs of the surfaces the light will bounce off of
Visibility to the light source (Think the back of a deep cave)
etc.


You could use some kind of formula to get an approximate value, based on these factors, but, in my opinion, it's simpler just to do it manually per scene. Or, you can remove it entirely, and use more sophisticated methods to calculate indirect lighting.