十之八九 is a probability adverb — 'eight or nine out of ten,' i.e. ~85% likely. Stronger than 可能 kěnéng (maybe) and 也许 yěxǔ (perhaps); softer than 一定 yīdìng (definitely). Often pre-modifies a verb phrase: 十之八九会迟到 = he'll most likely be late.
memory
Literally 'of ten, eight-or-nine.' 之 is the classical possessive — read it as English 'of': out OF ten, eight-or-nine. The same structure appears in 百分之八十 (80%) and 三分之一 (1/3).
