Understanding the Problem
To find the probability that three randomly selected children have different birthdays, we need to consider the total number of possible birthdays and the favorable outcomes.

Total Birthdays
- Assume there are 365 days in a year (ignoring leap years).

Total Possible Outcomes
- For three children, the total number of ways their birthdays can be assigned is \(365 \times 365 \times 365 = 365^3\).

Favorable Outcomes
- For the first child, there are 365 choices.
- For the second child, to have a different birthday, there are 364 choices.
- For the third child, to have a different birthday from the first two, there are 363 choices.
- Therefore, the number of favorable outcomes is:
\[
365 \times 364 \times 363
\]

Calculating the Probability
- The probability \(P\) that all three children have different birthdays is given by:
\[
P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{365 \times 364 \times 363}{365^3}
\]
- Simplifying this, we get:
\[
P = \frac{364}{365} \times \frac{363}{365}
\]

Final Probability Value
- Calculating that, we find:
\[
P \approx 0.9918 \text{ or } 99.18\%
\]
Thus, the probability that three randomly selected children have different birthdays is approximately 99.18%.