Statistics and Probability: JEE Main 2021 Mathematics question

Let B_i (i = 1, 2, 3) be three independent events in a sample space. The probability that only B₁ occur is $\alpha$, only B₂ occurs is $\beta$ and only B₃ occurs is $\gamma$. Let p be the probability that none of the events B_i occurs and these 4 probabilities satisfy the equations $\left( {\alpha - 2\beta } \right)p = \alpha \beta$ and $\left( {\beta - 3\gamma } \right)p = 2\beta \gamma$ (All the probabilities are assumed to lie in the interval (0, 1)). Then ${{P\left( {{B_1}} \right)} \over {P\left( {{B_3}} \right)}}$ is equal to ________.