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This sounds very concerning. This is not typical for arthritis. Usually with arthritis you notice subtle signs over the course of months. Such signs may include difficulty rising, difficulty with stairs, stiff gait, slipping/falling down sometimes on slick surfaces.
What you are describing with more of an acute onset sounds like it may be a back/spine problem. This causes a dog to lose the ability to know where their legs are. When only the hind limbs are involved this suggests a problem in the lumbar spine. In a dog of her age it could certainly be 1 or more slipped disks (intervertebral disc disease), but I also worry about a tumor. The best next step would be to take her in to see her veterinarian for a good physical exam. This will tell us if it is a nerve problem. If so, your vet will likely recommend radiographs (x-rays).
This being said, it is always possible that your dog does have arthritis and had an accident yesterday in which she hurt herself and now has a more difficult time. This would be best case scenario. Still warrants a trip to the vet to have a good physical exam and x-rays.
Best of luck. I'm hoping for arthritis with acute exacerbation.