8. Each vertex of a regular nonagon is equally likely to be painted one of two colors, red or blue. The probability that there exist three vertices of the same color forming an acute triangle is $\qquad$ .
If the convex polygon formed by vertices of the same color contains the center of the circumcircle of the regular nonagon, then there exist three vertices of this color that form a triangle also containing the center, which means this triangle is an acute triangle. Conversely, if a color's vertices contain the vertices of an acute triangle, then the convex polygon they generate contains the center of the circumcircle of the regular nonagon, as shown in the figure.
In this way, if the convex polygons generated by the red and blue vertices do not contain the center, then the vertices of these two colors should each lie in the corresponding semicircles of the circumcircle defined by the same diameter.
The only possibility for this to happen is that the red points are 4 consecutive vertices or 5 consecutive vertices, each with 9 cases. Let $E=$ “there exist three vertices of the same color forming an acute triangle”, then $P(E)=1-P(\bar{E})=1-\frac{18}{2^{9}}=\frac{247}{256}$.