Depending on the context, this could also mean interest in a woman named 'Ζωή'
If we were talking about an actual person named Ζωή, be sure that the name would be capitalized, so you can tell it apart. xD
"Το ενδιαφέρον για τη ζωή. " its the correct answer no "Το ενδιαφέρον για την ζωη