A Vector Condition on a Regular Octagon

In the coordinate plane $xOy$, $O$ is the centre of a regular octagon $A_1A_2\cdots A_8$ with $A_1=(1,0)$. Two distinct vertices $A_i,A_j$ are chosen, and point $P$ satisfies $\overrightarrow{OP}+\overrightarrow{OA_i}+\overrightarrow{OA_j}=\vec 0$. Find the probability that $P$ lies in the first quadrant.