Answer:
I use nearly the same ratio to substitute for most herbs. 3 to 1. You want one third the amount of dried as the amount of fresh that is called for. That would be approximately 1 teaspoon of dried to one tablespoon of fresh, or 1/3 cup of dried for your 1 cup of fresh. However, it also depends on how fresh your dried herbs are. Fresher dried herbs will have a stronger flavor and you may be able to use less. Older dried herbs will have a weaker flavor and may require more.
If the parsley is to be used as a garnish, I wouldn't substitute dried.