this is my opinion..
believes in means that you have faith in something..
i.e I believe in you. same as i have faith in you./ i trust you
as for believe.. i think that there must be some kind of explanation to stress out why did you choose to believe.
i.e i believe you, because you are my friend.
She believes me as we've known each other for quite some time.
but still for above poll, the correct most matched answer would be 'believes in'. =)