Consider a market with $\Omega= (\omega_1, \omega_2, \omega_3)$, $r = 0$ and one asset $S$.
Suppose that $S(0) = 2$ and $S$ has claim $\bar S = (1, 3, 3)$ at time 1.
Find all the risk-neutral probability measures on $\Omega$
What I did for this question is construct a similar table as in Sure Thing Arbitrage. I got a system of solutions which gave
$\Bbb Q=(\frac{1}{2}, p, \frac{1}{2}-p)$ as the set of all possible risk neutral probability measures. But again, I am not sure if I can take the claims at time 1 to be the same at the price/value of the asset at time 1.