We have a random variable $Y_n$ stochastically bounded, so for each $\varepsilon \geq 0$ , $\exists$ a constant $K$ and a value $n_0 = n_0 (\varepsilon)$ such that $P(\left | Y_n \right |\leq K) \geq 1- \varepsilon$ . So we now consider another random variable $X_n$, and we know:
$$ \frac{X_n}{Y_n} \overset{P}{\rightarrow} 0 \textrm{ when }n \rightarrow \infty $$
And we want to prove:
$$ X_n \overset{P}{\rightarrow} 0 \textrm{ when }n \rightarrow \infty $$
So i found out that there is a question with a correct answer about this topic, but that answer starts with this:
$\left | X_n \right | > \varepsilon$ implies that $\left | \frac{X_n}{Y_n} \right | \geq \frac{\varepsilon}{M}$ or $Y_n\geq M$. It says that we can prove this by contradiction but i do not understand how.