Can ants sense food from a long distance?
Ants follow odor cues in the wind.  A study by Wolf and Wehner (2000) manipulated ant antennae and wind direction to show that ants followed odor plumes on the wind. A more recent study by Buehlmann et al. (2014) showed that desert ants of the genus Cataglyphis cued in on linoleic acid, a so-called necromone (death scent) released by dying insects. Here's a popular article that summarizes the latter study.  Chances are good the ants are followed the odor plumes coming from your mostly empty food container.

Literature Cited

Buelhman, C. et al. 2014. Desert ants locate food by combining high sensitivitty to food odors with extensive crosswind runs. Current Biology 24: 960-964.

Wolf, H. and R. Wehner. 2000. Pinpointing food sources: Olfactory and anemotactic orientation in desert ants, Cataglyphis fortis.  Journal of Experimental Biology 203: 857-868.