Even if there's no food, ants will still come in for water.
Best way to kill them is with boric acid. Just do a google search for "boric acid ant bait" and you'll get a whole slew of recipes. Boric acid is readily available for cheap at any pharmacy or hardware store, it's a relatively harmless white powder (don't eat it though, heh). What you do is mix the boric acid in with sugar water or peanut butter (depending on whether you have sugar ants or grease ants) and set the bait out for the ants. The ants will find it and swarm it, leave them alone. What they're doing is taking the sweet, sweet poison back in small quantities, and feeding it to their queen. Eventually, after about 24 hours, the poison levels will build up in their little bodies so it wipes out the whole colony, queen and all. You'll know when that happens, because the bait that was previously the ant version of Old Country Buffet will become totally empty. No more ant problem (well, at least not until another colony moves in a couple months later and you have to repeat the process).