Can you say more about what you mean by "unconditional probability"? You can get the predicted probabilites of the outcome for the data used to fit the model by running predict(my_model, type="response") (where my_model is the probit model object returned by the glm function). You can get predicted probabilities for new data by providing a new data frame to predict that has values of the independent variables at which you want predictions, for example, predict(my_model, newdata=my_new_data, type="response").
If you're interested in marginal effects, you could look at the margins package, which has functions for extracting marginal effects from generalized linear models.
We can provide help specifically tailored to your problem if you can provide a data sample and the code you ran (see here for help on how to provide a reproducible example).