"He is in prison."
Translation:Hij zit in de gevangenis.
For being incarcerated zitten is always used. This usage is so clear that sentences like: Hij/zij moet zitten usually this will mean He has to do time (since there aren't that many situations where you're mentioning that a 3rd person has to sit).
If you're visiting a prison building, you could say: Ik ben in de gevangenis. You cannot leave out de in this kind of sentences, I'm not sure why, but to me it's similar to English I'm at the bank. The only similar sentences I can think of now, where you can leave out the article in Dutch are: op school and op kantoor.