Belief in magic is kind of hard to define, anthropologically—we tend to call anything that contradicts currently-known laws of physics “magic”, but that makes the term contingent on the observer’s knowledge rather than the believer’s. (For instance, things like astrology and alchemy that we regard as magic now were thought to be the result of natural forces in the Middle Ages.)

I would call magic the belief that there are multiple, independent systems of causality, whether you fully understand those systems or not.