Discrete Bayes Filter: One Measurement Update

A robot moving along a 1D hallway estimates which of 3 discrete cells it occupies. Its current belief (prior) over cells $(c_1, c_2, c_3)$ is $(0.2, 0.5, 0.3)$. A door sensor fires, and the likelihood of getting this exact sensor reading given the robot is in each cell is $P(z \mid c_1)=0.6$, $P(z \mid c_2)=0.2$, $P(z \mid c_3)=0.9$. Applying one discrete Bayes filter measurement (correction) update, what is the posterior probability that the robot is in cell $c_2$? Give your answer as a probability (round to 2 decimal places).