Let there be three independent events \( E_1, E_2 \) and \( E_3 \). The probability that only \( E_1 \) occurs is \( \alpha \), only \( E_2 \) occurs is \( \beta \) and only \( E_3 \) 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 \( \dfrac{\text{Probability of occurrence of }E_1}{\text{Probability of occurrence of }E_3} \) is equal to ________.
