In ancient times, there were 8 million gods (Yaoyorozu no kami) in Japan.
At that time, there were dogs that looked the same that we can see now but they only had three legs. That’s how they were designed for some reason. Of couse it was awkward to walk and run.
One day, one dog begged to one of 8 million gods to give them a fourth leg.
The god understood the circumstance and started thinking.
“I can give you a fourth leg but I have to subtract it from something else. What will it be? A thing which already has an extra leg.”
He looked at a censer at the corner of his prayer room. “This is it!”
He pulled one leg from the censer and attached it to the dog. “Hmm, both look good!”
That is why censers only have three legs and dogs have four legs.
Dogs are still care of the fourth leg from the god and when they pee they lift the leg try not to wet.