Charge resides on the outer surface of a conducting hollow sphere of radius $R$. We consider a spherical surface of radius $r<R$.

By Gauss theorem



${\int }_{\text{s}}\overrightarrow{E}.\mathrm{d}\overrightarrow{s}=\frac{1}{{\epsilon }_0}\times$ charge enclosed

$E\times 4\pi r^2=\frac{1}{{\epsilon }_0}\times 0\Rightarrow E=0$

i.e. electric field inside a hollow sphere is zero.