A set of three points is chosen randomly from the grid shown. Each three-point set has the same probability of being chosen. What is the probability that the points lie on the same straight line?

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for (int i=0; i<3; ++i) {
for (int j=0; j<3; ++j) {
dot((i,j));};}
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The number of three-point sets that can be chosen from the nine grid points is \[
\binom{9}{3} = \frac{9!}{3!\cdot 6!} = 84.
\]Eight of these sets consist of three collinear points: 3 sets of points lie on vertical lines, 3 on horizontal lines, and 2 on diagonals. Hence the probability is $8/84 = \boxed{\frac{2}{21}}$.