"strong suspicion" means having a strong belief or feeling that someone or something is likely guilty or responsible for something, even without having definite proof. Full definition
My very strong suspicion is that half of everything they sell is made with petroleum products. (americanenergyalliance.org)
He is a bearded Midwesterner with strong suspicions that a small group of politically connected climate scientists are influencing their community's behavior. (polluterwatch.com)
is not at all mitigated by the even stronger suspicion that he said the same thing during Spielberg's War of the Worlds (running non-combatants get toasted from above) and Matt Reeves's Cloverfield (civic landmarks wrecked by an animal - shaped alien invader). (slantmagazine.com)