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 $\left(n_1,n_2,n_3\right)$ is an outcome, $\left(1\le n_1\le 6\right)$ and is found to satisfy the equation $i^{n_1}+i^{n_2}+i^{n_3}=1$, , then the probability that a fair die was thrown is (where $i=\sqrt{-1})$

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