Next, the solution to the puzzle posed in the first column. The indiatimes.com link to the first column is here. You can view the puzzle itself on the indiatimes site. What follows is the full, unabridged, complete solution to the puzzle and so, if you are just here to check your answer to the puzzle, the answer we were looking for was just this : 0.5. Three characters to type out. That's all, folks.
No, wait. We wouldn't be a real puzzle column if we didn't post the correct solution to the puzzle as well as a proof of correctness, and so what follows is a detailed derivation of the solution and an accompanying proof.
In solving this puzzle, let us see if we can derive a solution for the problem when there are N passengers on Chandrayaan for some arbitrary N greater than 2. In investigating the solution to the problem, we can start off by trying to solve this for N = 2.
When there are just two passengers on the shuttle, the solution is simple. The first passenger may pick either Seat #1 or Seat #2. If the passenger picks Seat #1, then you, as the final passenger, will get your seat for sure (probability = 1.0). If the passenger picks Seat #2, then you will certainly not get your seat (probability = 0.0). So, the probability for N = 2 is clearly one half.
Let us now see if we can solve it for N = 3. When there are three passengers, the first passenger may pick Seat #1, #2 or #3 with equal probability. If the passenger picks Seat #1, then again, you, as the final passenger, will get your seat for sure (probability = 1.0) since Passenger 2 will pick Seat #2. If the passenger picks Seat #3, then you will certainly not get your seat (probability = 0.0). The average of that is again one half. Now, that leaves the case where Passenger #1 picks Seat #2. If this happens, Passenger #2 is now in the position of either picking Seat #1 or Seat #3. But this situation is exactly the same as that where N = 2. The probability of you, as the final passenger, getting your seat is half. So, the net probability is (1/3*1.0 + 1/3*0.0 + 1/3*0.5) = 0.5. So, again the probability of N = 3 is one half.
Update (Mar 21): Updated the post a bit.