First, you pick is not defective with a probability of 17/20, the second with a probability of 16/19, the third 15/18, and the fourth 14/17.
So the probability of picking no defective tyres is:
(14*15*16*17)/(17*18*19*20)=168/342=84/171
So the probability of picking at least one defective tyre is 87/171 (just over half).