When both versions are available, the logic is pretty straightforward: const version is called for const objects, non-const version is called for non-const objects. That’s all.
In your code sample a is a non-const object, meaning that the non-const version is called in all cases. The const version is never called in your sample.
The point of having two versions is to implement “read/write” access for non-const objects and only “read” access for const objects. For const objects const version of operator [] is called, which returns a const double & reference. You can read data through that const reference, but your can’t write through it.