How can you identify the anode and cathode of a car battery of indistinct shape by using a potassium iodide solution? Now I know that the anode in a car battery is lead, the cathode is lead dioxide and the electrolyte is sulfuric acid, but still: how could a potassium iodide solution be used to differentiate between the anode and the cathode?

I mean, lead can't replace potassium in its salt because it lies below it in E.C.S., so how are we supposed to identify them by using potassium iodide?
By using the battery as a source of electricity in an electrolytic cell that contains potassium iodide as an electrolyte.
Electrolysis takes place where iodide ion is oxidized at anode and brown colour of iodine solution appears at anode.
At cathode hydrogen gas evolves which is indicated by formation of bubbles at cathode.