A coin is tossed. If head appears a fair die is thrown three times otherwise a biased die with probability of obtaining an even number twice as that of an odd number is thrown three times. If $\left({\mathrm{n}}_1,{\mathrm{n}}_2,{\mathrm{n}}_3\right)$ is an outcome, $\left(1\le {\mathrm{n}}_1\le 6\right)$ and is found to satisfy the equation $i^{{\mathrm{n}}_1}+i^{{\mathrm{n}}_2}+i^{{\mathrm{n}}_3}=1,$, then the probability that a fair die was thrown is (where $\mathrm{i}=\sqrt{-1}$ )