Belief has very little to do with how placebos work.
Placebos work on people who have been told that the treatment they are receiving is sham. The most likely explanation for this observation is classical conditioning, which occurs in people independent of their thoughts and beliefs. One example of this is the production of hay fever symptoms in people who have allergies by exposing them to plastic flowers. The subjects knew that the flowers were plastic, yet still showed hay fever symptoms.
Here is another interesting study :
Surprise Finding About Placebo Performance - CBS News
Often, the interaction with the people giving the placebos and all the ritual surrounding the "treatment" is probably more important than the placebo itself. I think this is why chiropractic, being "born again", reiki and homeopathy can produce testimonials of such profound effects.
I think people often underestimate the extent to which our perceptions can be manipulated.