You have four tires A,B,C & D. The first student picks a tire, any tire--the reminin three students pick the same tire.
The possibilities are
AAAA, BBBB, CCCC & DDDD
the first students pick is 4/4, the remaining three are 1/4
AAAA is 1/4^4, BBBB is 1/4^4, CCCC is 1/4^4 & DDDD is 1/4^4
adding them up is the P(E), 4(1/4^4)=1/4^3