For speakers of North American English... 'in the hospital' means you are sick and are being treated in a hospital. When you are a visiting or are there for a check-up, you are 'at the hospital'. Example: Tom is in the hospital with two broken legs. Susan is at the hospital visiting him. 'In hospital' is not used *at all* in North American English, and it sounds incorrect or strange to our ears. If you use this term with speakers of NA English...be prepared to be corrected! :-)

'In the hospital' just means that you are inside the hospital building. Perhaps you've gone there for a check-up, or to visit a sick friend. We don't know why you are there - all we know is that you are inside this building. 'In hospital' has a much more precise meaning. It means that you're a patient. You have been admitted by the medical staff for treatment. You've probably been assigned a bed and will have to stay overnight, and you probably can't leave until a doctor has signed the documents to say you've been discharged. The same distinction applies to prisons. A person who is 'in prison' is an inmate ( in other words, a prisoner), while a person who is just 'in the prison' could be in the building for any reason. NB. A regional footnote : Speakers of American English don't seem to observe this distinction.

correct