Picking is something that can have a lot of root causes - it can also be a hard habit to break. Were they with a rooster at their previous home? Were they housed in a closed up, maybe crowded, sort of unit or were they free ranging? What were and are they being fed? Picked spots invite picking - similar to how a small injury can draw attention and further pecking until a tiny wound is a large, serious wound or dead bird.
For the short term, a good way to protect the exposed area to allow for regrowth and prevent sunburn is a "hen saddle" - it will cover the exposed area. They are readily available for purchase online from many outlets or you can even find DIY instructions for making your own.