If you are missing only one of three eggs, you might have an egg eater but then you might have a different problem. If a predator eats an egg, the chickens will usually clean up the shell. I'm thinking mainly a rat but it could have been something else like a possum or a skunk.
It is possible that the egg was accidentally broken and the chickens cleaned it up. That does not mean you have a chicken that is intentionally cracking the eggs to eat them, but it is a big step toward them learning to eat eggs. Do your nests have a lip on them to keep the eggs and bedding material from falling out? Maybe a hen stepped on it.
It's hard to tell what is going on. Rusty could be very right. I'd suggest the fake eggs. Don't leave real eggs in the nests for any longer than you have to. Eggs left in the nests increases the opportunity for accidents and can attract predators.