Do hawks eat woodpeckers

I just saw this today. A smaller hawk (one of the babies in the hood), was eating one of my woodpeckers (the family that lives in the tree by my deck). I did not think that hawks eat birds, especially with all the rabbits and squirrels around this area; but I definitely saw it, and watched it for some time (picking out the feathers and then to the good stuff). The woodpecker was a full size one, not one of the babies. The woodpeckers are the black and white ones, and some have the red crest on their heads!