I'm in the middle of a "The Fishing Job" quest for the thieve's guild and I have been told to steal Danica Pure-Spring's Gold Diamond Ring. However when I attempt to steal this ring it says that there is a 0% chance of stealing it. Any help would be greatly appreciated!

Take it anyways.

If you fail, just quit the job.

save the game.
paralyze her with the paralyze spell. (make sure you are not seen)
use a calm spell to remove her hostility.
keep trying to pickpocket her while she is paralyzed and eventually you can pickpocket her.
the paralyze effect will wear off and her inventory will open (if you are still pressing activate)
no matter what the percentage is for the pickpocketing, you will be able to take the item.

Did you use a potion? Are you wearing any pickpocket enchanted gear?

Try using the Calm spell if you have it on her and then pickpocket.

You need to put some perks into pick-pocketing before you start trying to steal things with value like that. I would just quit the job, and then start doing fishing jobs when you get some higher skill into pick-pocketing. The Blackguard armor, and Thieves Guild Master armor give very good pickpocketing bonuses too. Or just do what Michaelpk said.