Odds of seeing a Milky Way supernova

Let’s say we find out there’s a supernova somewhere in the Milky Way galaxy (thanks to neutrino detectors). Certainly everyone would be excited if it were say Betelgeuse, but more realistically it could be anywhere in the galaxy, including behind some giant cloud of dust. What are the odds, considering how much of the Milky Way is obscured by dust vs. how bright a supernova would be, that we would be able to observe it?

Also assuming we got an early warning from neutrino detector like SuperK or IceCube, how precisely would that tell us where to look in the sky? (I suppose if it were at all visible something like ZTF would pick it up on its own?)