Like I said not all types of mange are contagious. EVERY dog has Demodectic mites in their hair folicles just as every human has them in our eyebrows!
Even sarcoptic mange could of been brought on your property from another animal coming onto your property & rubbing against a bush & then your dogs rub against the same bush. Just because you or dogs haven't been in direct contact with it doesn't mean they won't get it.
Yet again I doubt it any type of mange as "usually" the symptoms start towards the head & feet but you never know.

Same thing goes with ringworm, you or your dogs may not have had contact but it could of been brought in by your shoes or outside from another animal somewhere.

I highly doubt it was caused by your ferret either. I have 4 ferrets and 3 dogs and never heard or seen of such a thing. I also have a lot of friends with ferrets & dogs & I have been speaking with them the last hour or so and none of them has of anything like that either.
If you are talking about the ferrets feces being the cause, well that is even more unlikely, in fact it is probably better for your dog than him eating any other feces or the like, that is *unless* your ferret is not getting the proper food. Ferrets are 100% carnivores, they have no cecum therefore can not digest anything but meat.

The cause could be one (or more) of many things. It shouldn't be more than maybe $30-40ish for an exam & a skin scrape to find out what the cause is.

Once you know the cause we may be of some more help.
Like ringworm can be treated with athletes foot creams & sprays (sprays seem to work better) instead of the baths & pills that most vets try to sell you to make more money.