To determine the probability of picking a three-digit number divisible by 7, first calculate the total number of three-digit integers, which ranges from 100 to 999, totaling 900 possibilities. Next, identify how many of these numbers are divisible by 7; this can be done by dividing the range's endpoints by 7. For example, from 1 to 70, there are 10 numbers divisible by 7, illustrating the method. Finally, calculate the percentage of three-digit numbers that are divisible by 7 to find the probability. This approach provides a clear framework for solving the problem.