9. A wire of length 1 is cut into three pieces. Then the probability that these three pieces can exactly form a triangle is
9. $\frac{1}{4}$.

Let the three segments be of lengths $x, y, 1-x-y$. Then the total sample space is $x>0, y>0, x+y<1$. The area of the region where the triangle can be formed is $x+y>\frac{1}{2}$, with an area of $\frac{1}{8}$.
Thus, the required probability is $\frac{1}{4}$.