Distinctions in the meanings of these words have broken down somewhat, but careful speakers continue to observe them. Apt suggests fitness or tendency: "Jake is apt in physics." Liable implies exposure to something unwanted, disadvantageous, or burdensome: "The driver is liable for damages." Likely means "expected," "probable": "It is likely to rain today." Likely is the most commonly used of the three words; apt and likely are near-synonyms; use liable only in the sense of "responsible," "answerable."
Dictionary of problem words and expressions. Harry Shaw. 1975.