Where does the prior p(y) come from when implementing Gaussian Discriminant Analysis?

I've been trying to work out for a while what the value of the prior p(y;ϕ) should initially be when solving a Gaussian Discriminant Analysis problem. I am aware that this is "the probability of y (the hypotheses) before we know the data" parameterized by ϕ - how would i go on to get the values for this?

To explain what I mean, I am aware that when we maximize this log likelihood formula.

we obtain the Maximum Likelihood parameters which are given by these definitions.

and with these parameters (mu and sigma), we can obtain p(x|y). However, my question is, what is the value for p(y;ϕ)? Is it just ϕ? Or what formula is used to compute the probability of y parameterized by ϕ?

Thank you very much for your help :) Best wishes!