第 035 题 / 45

一位飞镖运动员向一个目标投掷三次,记事件 ${A}_{i} =$ “第 $i$ 次命中目标” $\left( {i = 1,2,3}\right) ,P\left( {A}_{1}\right) = \frac{1}{8},P\left( {{A}_{i + 1} \mid {A}_{i}}\right) = {2P}\left( {A}_{i}\right)$ , $P\left( {{A}_{i + 1} \mid \overline{{A}_{i}}}\right) = \frac{1}{8}\left( {i = 1,2}\right)$ ,则 $P\left( {A}_{3}\right) =$ ___.