  We study the contextuality of a three-level quantum system using classical
conditional entropy of measurement outcomes. First, we analytically construct
the minimal configuration of measurements required to reveal contextuality.
Next, an entropic contextual inequality is formulated, analogous to the
entropic Bell inequalities derived by Braunstein and Caves in [Phys. Rev. Lett.
{\bf 61}, 662 (1988)], that must be satisfied by all non-contextual theories.
We find optimal measurements for violation of this inequality. The approach is
easily extendable to higher dimensional quantum systems and more measurements.
Our theoretical findings can be verified in the laboratory with current
technology.
