Conductivity of electricity is an important property of water and it is well established that water exists in 3 fundamental forms of matter, i.e. ice, liquid water and gas as water vapours. How does water in crystallised form (ice) conduct electricity?

The water vapours do not conduct electricity due to inefficiency of transfer of electrons or charges. Ice on the other hand, even being a closed lattice with zero entropy, conducts electricity through proton hops where a proton jumps from one molecule of water to another making it charged. This is done by quantum tunnelling, which is why the conductivity is fastest in case of ice.