Let $\mathrm{B}_i(\mathrm{i}=1,2,3)$ be three independent events in a sample space. The probability that only $\mathrm{B}_1$ occur is $\alpha$, only $\mathrm{B}_2$ occurs is $\beta$ and only $\mathrm{B}_3$ occurs is $\gamma$. Let p be the probability that none of the events $\mathrm{B}_i$ occurs and these 4 probabilities satisfy the equations $(\alpha-2 \beta) \mathrm{p}=\alpha \beta$ and $(\beta-3 \gamma) \mathrm{p}=2 \beta \gamma$ (All the probabilities are assumed to lie in the interval $(0,1)$ ). Then $\frac{\mathrm{P}\left(\mathrm{B}_1\right)}{\mathrm{P}\left(\mathrm{B}_3\right)}$ is equal to $\_\_\_\_$ .