Going back to your original question. If one of the ceiling bulbs burns out, the others will continue glowing unaffected.
But if you were powering 3 small light bulbs off a couple of C cells, and one of the bulbs burnt out, you would probably notice the other two glow a tiny bit brighter, because with fewer bulbs to power, the battery would be supplying slightly more voltage. That's a characteristic of batteries: the more current you draw from them, the lower (slightly) the voltage the battery puts out.