Translation from Bayes formula elements to brms elements

I spent quite some time reading your papers on the package but I am unfortunately still having some trouble relating the syntax of the package to the elements of my Bayesian formula, and I was hoping that you might be able to give me a few pointers.

A brief outline of my model: I conducted two surveys with three groups of participants each. In the surveys each participant rated the probabilities of 20 events on a scale from 0 to 100.
In my previous analysis I assumed that the likelihood for each data point followed a gauss distribution centered on a parameter (rho) and (for simplicity) that the probability of each individual response was independent from all other responses. The prior for rho was also a gauss distribution with specified width.

What I want to do now is to change this model to a hierarchical model, where the answers of a single participant are possibly correlated. My plan is to assign each participant i an individual parameter rho_i, where the rho_i follow a gauss distribution around rho.

Could you show me how to translate each of these setups (both simple and hierarchical) into the brms code, possibly with a few general comments on how the syntax relates to the elements of Bayes’ formula?

Thanks in advance.

The simple model would just be

brm(y ~ 1, ...)

and the multilevel model would be

brm(y ~ 1 + (1 | participant), ...)

if I understand you correctly.