There are technologies currently in existence and that are very close to being reality, that can turn sea water into perfectly fresh drinking water or 'medical grade' water
We do this now. Nimitz class super-carriers desalinate about 400 thousand gallons of water a day. For that matter, any aircraft carrier would be ideal in a zombie apocalypse. They are already setup to desalinate water, they can house a large population(especially in the case of a Nimitz), they have weapons and ammo storage, and ITS A FUCKING AIRCRAFT CARRIER!