Adobe programs generally support Postscript formats for printing purposes and thus can also import them for further use. Your best bet for eps to ai conversion would be to use Adobe Illustrator, the original program for AI format.
This will typically only work for vector graphics / rich documents that were exported to EPS format either in Illustrator itself or similar program.
You can also try one of the 3rd party alternatives, but AI format is mostly closed and the latest version of the format is rarely supported except Illustrator itself.