The word "conspire" according to Webster:
"to join in a secret agreement to do an unlawful or wrongful act or an act which becomes unlawful as a result of the secret agreement"
So from this definition, we can see that to qualify as a conspiracy, an action must be agreed upon (meaning two or more persons), kept secret, and either illegal or immoral.
The paradox of conspiracy theories that the very act of learning about a conspiracy disqualifies it as still being a conspiracy, because it is no longer a secret once people know about it.
It seems to me that what "conspiracy theorists" are really searching for are stories about where truth overlaps with absurdity. Like the US taking in thousands of Nazis (the scientists who later gave way to NASA), or the FBI trying blackmail MLK Jr. into suicide, or the CIA trying to give people so much LSD that they could control the mind or induce ESP. None of these are conspiracies anymore. They were conspiracies, but now they are history.
So the next time someone says "Conspiracies don't exist", just smile, agree with them, then ask them I've they've heard about the time the US Navy tested their biological warfare systems on the population of San Francisco.