I made a Shape Key to fix the jaw.
I have tested it by moving the F-Curve and I can see it change when the value passed 1.
And when I go to pose mode and change the jaw bone and come back to the driver, I can see the driver value changed too.
So which means I have set the armature and bone right.
But the shape key just doesn't change at all!
I have to move the slider manually again for it to change.
So looks like the shape key's value itself was overriding the driver value for some reason!
Could somebody please be so kind and tell me what did I miss!?