believe in has a somewhat different set of meanings to believe. Here is the information from the Oxford Dictionary
1. Accept that (something) is true, especially without proof
the superintendent believed Lancaster’s story
[with clause]: some 23 per cent believe that smoking keeps down weight
1. Have faith in the truth or existence of
those who believe in God
- I believe that John will be acquitted in the end.
This statement works fine with the believe meaning: you accept that something is true.
- I believe in John's being acquitted in the end.
This sentence is grammatically correct but does not feel right because it suggests some kind of religious or idealistic faith in the outcome.
Things that you can believe in are God, justice (as an abstract concept), progress, and of course Father Christmas and the tooth fairy.