Statistics and Probability: JEE Main 2021 Mathematics question

Let there be three independent events E₁, E₂ and E₃. The probability that only E₁ occurs is $\alpha$, only E₂ occurs is $\beta$ and only E₃ occurs is $\gamma$. Let 'p' denote the probability of none of events occurs that satisfies the equations ($\alpha$ $-$ 2$\beta$)p = $\alpha$$\beta$ and ($\beta$ $-$ 3$\gamma$)p = 2$\beta$$\gamma$. All the given probabilities are assumed to lie in the interval (0, 1). Then, $\frac{Probability\ of\ occurrence\ of\ E_{1}}{Probability\ of\ occurrence\ of\ E_{3}}$ is equal to _____________.