opportunity and possibility
We often say that somebody has the opportunity to do / of doing something.
- I have the opportunity to go to Denmark next year. (= I can go …)
Possibility is not often used in this structure. It is more normal to say that there is a possibility of something happening.
- There’s a possibility of my going to Denmark next year. (= I may go …) (More natural than I have the possibility to go to Denmark …)