Check for lice/mites after dark with a flashlight. They and their eggs are tiny, at the base of the feathers or on the feather shafts.
I would go ahead and treat for lice/mites with Sevin dust. Lice/mites are transferred from wild birds easily. Most likely you will always have a few around; it's a matter of controlling the numbers, not eradicating a pest once and for all.
I doubt that rats are picking feathers, as they will chew on the animals (and humans, as well, for that matter.) But there are probably some around, unless you have a very good preventive program in place, like lots of barn cats that love to eat them.
If you don't spend a lot of time with them, I would find some time to just watch their behavior for a while. If you have a feather picker, you will see the behavior, but not necessarily in a few minutes.
I believe I would attack it with all 3 approaches, since there are most likely mice/rates and lice/mites around, anyway, and I wouldn't be surprised to learn you have one or two that are picking feathers, as well.
Probiotics are always good, even with a healthy flock, and especially with any health problem going on.
If you have a feather picker, you will almost always find that only some chickens get picked. Has to do with pecking order.
I see your run has no grass or weeds. If they are there at all times, you might give some clumps of dirt with grass/bugs for them
to peck at, along with some other distractions like a hanging head of cabbage or some melon rinds. I believe I also see guineas there. I have never had any guineas. It is possible they are the ones doing the attacking. Your chickens look to me like they are buff orps, though I am no expert on this. If so, they are known to be prone to being victims of bullies.
Low protein intake could also be a factor. It would help if we knew what they eat, and what their daily routine is like, including size of coop and run, and number of birds.