Probability Fundamentals & Geometric Probability · Challenge problem

Three different points are chosen at random from the $16$ points of a $4\times4$ square grid of lattice points $\{0,1,2,3\}\times\{0,1,2,3\}$, all $\binom{16}{3}$ choices being equally likely. What is the probability that the three points lie on a line? Express your answer as a common fraction.