It depends on the dog, but it's really quite rare that you can trust a single dog alone, let alone three. My 3 (two Shepherds and a Boston Terrier/Beagle) I would trust two, the boys. My girl? I'm pretty sure when she's twitching in her sleep it's because she's dreaming of the day I forget to lock the chickens up.
I've had 1 dog out of... what am I at now... 25? who I trusted with birds. Even raising them from puppies doesn't change their minds if they have prey drive of any kind. A Doberman and a Beagle, neither a rescue like most of the others, who proved that training and raising the dog and such will prevent an accident. One rooster to the Doberman because the rooster got into her area, 6 Call duck chicks killed and 3 pekins injured by the beagle in about 20 seconds.
But that one... he liked EVERY animal... he's a cool dog, my inlaws have him now. he went horse back riding with us and the goat (goat refused to be left behind!), he played with the rabbits. Really he watched the rabbits play with him, one would jump around and over him. Never seen a dog that could resist a jumping rabbit like that. He didn't even have an urge! And the baby ducks... OMG, he would let them sleep on him and he'd lead them around the yard and play daddy duck. 100% trusted that dog. His only vice? Squirrel chasing. Odd... that was the only time he showed any prey drive at all.
My male Shepherd? No prey drive. Watches the other two chase squirrels. He lays by the chicken run, watching. I'm not sure if he's guarding or contemplating something. He might be alright, I was going to do some leash training just to see. But trust him? Not until I see a rabbit jump over his head and him not even flinch, followed by him sleeping in a pile of ducks and acting like he's their daddy. LOL