You may not have rights, but you certainly can fight this (huge) smoking charge. The amount is something I would expect if you'd been chain-smoking cigars for hours. Quite ridiculous.
Compose a concise, polite email informing the hotel that you did not smoke in the room and asking them to remove the charge from your CC. Your tone should indicate that this is probably just a mistake, you're not accusing anyone of anything. Finding a cigarette package in the trash is not any kind of proof. Do you know that you left that package in your trash, or did they tell you they found it? If the hotel didn't bring it up, you can ignore it ... there are no rules against putting things in your hotel room trash can. Ask them to confirm that they processed the credit within 5 business days. If they push back, ask them for proof that you smoked in the room. If they don't respond at all, send another very polite email and tell them that you'll be forced to dispute the charge on your credit card if you don't hear from them in five business days. At all times, maintain a businesslike approach; the person dealing with this at the hotel did not cause your problem, and may be in a position to help you. Good luck, and please let us know the outcome.