# Obtaining posterior outcome probabilities Multinomial Probit given posterior parameter estimates

I'm trying to compute the individual posterior probabilities from my estimated multinomial probit model. I have obtained the latent utilities as well as the posterior parameters for beta and sigma for each individual, but now I am confused how to obtain the posterior probabilities.

For the binomial probit model it seems straightforward to obtain the posterior probabilities by calculating:

E[Φ(x'beta]

for each individual, where Φ represents the cumulative normal distribution . But I don't understand how to translate this to the multinomial scenario.