(i) To find the number of different arrangements for parking the 9 cars and leaving 4 empty spaces, we use permutations. The total number of ways to arrange 9 cars in 13 spaces is given by the permutation formula:

\(^{13}P_9 = \frac{13!}{(13-9)!} = \frac{13!}{4!} = 259,459,200\).

(ii) If the 4 empty spaces are next to each other, treat them as a single block. This reduces the problem to arranging 10 blocks (9 cars + 1 block of empty spaces). The number of arrangements is:

\(10! = 3,628,800\).

(iii) The probability that there will not be 4 empty spaces next to each other is the complement of the probability that they are next to each other. Thus,

\(P(\text{not next to each other}) = 1 - \frac{\text{arrangements with 4 empty spaces together}}{\text{total arrangements}}\).

\(P = 1 - \frac{3,628,800}{259,459,200} = 0.986\).