Step 1 :Consider all four-digit numbers that can be made from the digits 0-7 (assume that numbers cannot start with 0).
Step 2 :The total number of such four-digit numbers is calculated as \(7 \times 8 \times 8 \times 8 = 3584\).
Step 3 :The number of four-digit numbers that are less than or equal to 6000 is calculated as \(6 \times 8 \times 8 \times 8 = 3072\).
Step 4 :The probability of choosing a random number from this group that is less than or equal to 6000 is calculated as \(\frac{3072}{3584} = 0.8571428571428571\).
Step 5 :This is equivalent to the fraction \(\frac{6}{7}\) when rounded to four decimal places.
Step 6 :Final Answer: \(\boxed{0.8571}\) or \(\boxed{\frac{6}{7}}\).