Suppose you take 3 samples and report a 99% confidence interval for each dataset. How would you go about calculating the probability that all the datasets contain the true population mean? No other statistics are provided.
Well what you could say is that if you repeated this experiment of generating three 99% confiodence intervals independently many times, the percentage of the time that the three intervals will all include the true mean is $100\times .99^3$ which is what Stephane said and is I think what the author intended.
I'll be careful with this question and suggest you to be careful with the answers. Recall that a $100\alpha\%$ confidence interval DOES NOT MEAN that there is a probability $\alpha$ of finding the true mean in the interval: remember that the true mean, $\mu$, is in the interval or it is not. This mean is not a random variable and, therefore, we cannot associate probabilities to it: the statistic, on the other hand, is random.
With that stated, I don't know if your question really makes sense. For more information about what confidence intervals really are, please read this post!