The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature

Decreases exponentially with increasing band gap

The probability of electrons to be found in the conduction band of an intrinsic semiconductor $P(E)=\frac{1}{1+e^{\frac{(E-E_F)}{kT}}}$; where k = Boltzmann's constant

Hence, at a finite temperature, the probability decreases exponentially with increasing band gap.