It's not possible to say precisely what the odds of X drives going out in Y amount of time are, but it is safe to say that drive failures are not completely independent, as commonly assumed. Multiple disk failures in the same array within close temporal proximity are actually a fairly common occurrence.
Less than a month ago, we had 4 drives fail over the same weekend on one of our production servers (same RAID set), one after another. Almost as soon as we replaced one drive, another failed... we ultimately ended up replacing all 7 drives, to be safe.
One reason, as you mentioned, is that the rebuild process is disk-intensive, so there's a non-trivial chance that a disk teetering on the edge of going bad will be pushed over the edge and fail, as a result of the increased stress it's under in providing data to rebuild the new disk.
Another factor to consider is that all the members in a RAID array tend to be in the same physical environment, and subject to very similar physical stresses (heat, vibration, power fluctuations, etc.), which tends to result in a higher incidence of similar failure times than you'd see with disks in different environments.
And, if you're like most people, you probably just bought 4 identical disks from the same place, and ended up with 4 disks from the same batch, resulting in the 4 disks sharing identical manufacturing characteristics (any defects or anomalies during that manufacturing batch are likely shared across all four disks). So identical disks in an identical environment... makes sense that they might share other similar characteristics, such as when they fail.
Finally, there's the fact that disk failures are not normally distributed (as in a bell curve). They tend to have higher failure rates at the beginning of their lives (infant mortality), and after a long period of time, when they wear out and die due to the physical stresses they've been subjected to, with a relatively lower rate of failure int he middle (the bathtub curve).
So, yes, multiple drive failures in the same RAID array happen with some regularity, and is one of the reasons you always want good backups.