Thanks all for the interesting discussion. I understand the folly in my own solution (at the least!).
I'm summarizing some of the interesting posts for a reader who might come across this thread in future. Might be worthwhile to also check the initial set of solutions that attempted to solve the problem "directly" on the infinite plane (including my own). The solutions varied from 1, 0.75, 0.64.. Also, you can check a related discussion:
Didn't discuss the approach below much further, but same result as bonanova's (closest to simulation result):
Bonanova's solution:
Simulation results when trying over a square and a circle. Not the same result as what was predicted above, but close:
Counter example to Bonanova's solution, which may be one of the reasons why the simulation result is not the same as predicted:
One more counter example to Bonanova's solution:
karthickgururaj's post in Hands up! was marked as the answer
If the 1st person is not A, it is known within first two questions. I have annotated my solution with how the possibilities change with each question, see below (ABC means the possibility that, "A is sitting in chair 1, B in chair 2, C in chair 3").
