Why is it when I scratch one area on my body to relieve an itch, another area suddenly gets itchy right after?

Have you ever noticed that when you scratch or rub an area of your body to relieve an annoying itch, another area on your body gets itchy immediately right after? And when you scratch to relieve the second itch, a third itch follows elsewhere, and so on. I notice this most during the winter months, when the skin gets dry and itchy. But the same phenomenon occurs at other times as well. Why does this happen?