Well, first off, how big is the tank? That's a lot of fishies, and a carnivore like a snowflake can cause huge bioload problems.
You'll want to do an immediate and large PWC
to dilute that ammonia and Nitrite, and then consider the root problem. Your tank is producing more waste than the biological filter can handle. There are two ways to handle this. Reduce livestock (no one likes doing that) or increase biofilter. I don't know all the details of your setup, but an increase in surface area (sponge, bioballs, live rock) may be able to counteract the problem. This is the more complicated and expensive option. Because "just a little bit" won't cut it. I mean huge increase in rocks, fill a sump chamber with rock rubble, stick a sponge prefilter somewhere, etc.
My guess is that the tank is overstocked, and since predators eat infrequently, but large quantities, that's why you haven't had a problem until just now. The eel had not yet pooped.