If we consider break down in Zener diode, then potential across $R_3$ will be $10 \mathrm{V}$ and $R_1$ will be $2 \mathrm{V}$ .

So current in $R_3$ will be $i_3=\frac{10}{1500}=\frac{2}{300} \mathrm{A}$

and current in $R_1$ will be $i_1=\frac{2}{500} \mathrm{A}$

$\Rightarrow i_1<i_3$ , which is not possible

$\Rightarrow$ The potential difference across the Zener diode does not reach to break down voltage. So no current will flow through the reverse-biased Zener diode.