Kochen-Specker (KS) theorem denies the possibility for the noncontextual hidden variable theories to reproduce the predictions of quantum mechanics.A set of projection operators (projectors) and bases used to show the impossibility of noncontextual definite values assignment is named as the KS set.Since one KS set with a mixture of 16 rank-1 projectors and 14 rank-2 projectors was proposed in 1995 [Keaghan M and Peres A Phys.Lett.A 198 (1995) 1] for a three-qubit system,there have been plenty of the same type KS sets and we propose a systematic way to produce them.We also propose a probabilistic state-dependent proof of the KS theorem that mainly focuses on the values assignment for all the rank-2 projectors.