Believing in conspiracies or conspiracy theories is not necessarily a fixed state of mind and there is a spectrum of conspiracy theories. There are conspiracies that very quickly become obvious as conspiracies, there are others that are more obscure and take some digging, there are others that are only proven or become apparent after declassification of secret intelligence, and there are some that are never proven. But they all start with a suspicion of conspiracy based on some initial proof which then becomes confirmed with time. But at the unproven or unprovable end of the spectrum, the CT remains a CT because there is no concrete evidence either because the findings have alternative innocent explanations or because there are no findings, only postulates based on beliefs. This is where the crucial word in your question lies ‘believing’. CTs become a system of belief not that of finding the truth.