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 $\underline{\hspace{2cm}}$.