the possibiliy "to do something" or "of something"

[chance22]

There is little possibility to persuade the people to believe me.
In this sentence, should "of " be used instead of "to" after "possibility"? I was taught to use "the possibility of doing something" instead of "the possibility to do something".
But when I google on the internet, I find a title like: Guantanamo Bay: A Possibility to Help Out Haiti? So it seems possibility can also be followed by "to".
Are they different? Or the preposition after possibility is not very strictly used?
I'm really confused. Looking forward to your help. Thanks

 

[Kamila M]

I was taught the same as you, namely that after possibility we should use 'of', but on the net we can find really everything.