With mad cow, will uninfected cow populations spontaneously develop mad cow on their own? Or was the first mad cow protein a rare misfortune not likely to happen again? Or did the first mad cow protein come from something other than a cow?
The protein structure needs to have a mutation which gives it a propensity to occasionally misfold. That creates a chain reaction.
If this happens at a low enough rate then the underlying protein may become widely distributed in the population, and then it may only take a chance mutation or misfold to cause the cascade
The reality is we don’t know what the prime mover in any of these conditions are. Likely some combination of random occurance and possibly some other mechanism as well. For example, CJD comes from mad cow - so mad cow is transmissible, but scrapie seems to both arise spontaneously in flocks and be transmissible between sheep