As it turns out, a lot of researchers and thinkers are interested in this.
University of Miami political scientists Joseph E. Uscinski and Joseph M. Parent, in American Conspiracy Theories (2014: Oxford University Press), report that believers in conspiracies “cut across gender, age, race, income, political affiliation, educational level, and occupational status.”
(By the way, the four characteristics of a conspiracy theory, they say, are: “(1) a group (2) acting in secret (3) to alter institutions, usurp power, hide truth, or gain utility (4) at the expense of the common good.”)
As to why, some researchers have found that feeling anxiety or a loss of control triggers conspiratorial explanations. So disasters and stressful situations (a terrorist attack, unemployment, even a big storm) very naturally prompt them. By trying to make sense of what's going on, people may "connect dots that aren’t necessarily connected in reality,” says Dutch researcher Jan-Willem van Prooijen.
People are also prone to various cognitive biases, including “confirmation bias” (an inclination to give more weight to evidence that supports what we already believe and ignore evidence that contradicts our beliefs); “proportionality bias” (a tendency to assume that big events have big causes); and "projection” (people who endorse conspiracy theories may be more likely to engage in conspiratorial behaviors themselves, and if they do it, they might assume that others do too.
And then there's U.S. philosopher, Linda Zagzebski, who chalks it up to what she calls intellectual vices: gullibility, carelessness, closed-mindedness, negligence, idleness, rigidity, obtuseness, prejudice, lack of thoroughness, and insensitivity to detail.
The best predictor of believing in a conspiracy? Believing in another conspiracy.