The situation you describe is not normal.
A friend of mine had a similar problem with his HP laptop (I don't remember the model, sorry, but it's <3 months old). HP had already replaced his battery once but the problems (rapid discharge) remained.
Turned out that the battery just wasn't quite seated correctly. Everything looked ok, but there was some electrical connection that wasn't making good contact.
Take your battery out, clean the contacts with a soft dry cloth and then carefully re-seat the battery. See if that works for you.
If not... call HP, get a new battery. If that doesn't fix it, they will probably need to look at your laptop.