How can I deal with this kind of categorical data in preprocessing?
You are asking what could be done in terms of preprocessing the data when one of the categories in categorical feature is very frequent. In such case nothing should, or even can, be done. In such case for many samples you observe the same value. If you transformed the values in some way, nothing would change about the fact that still many samples have the same category (while it would be encoded using different value). Saying it differently, if you changed the encoding of classes, the only thing that would change is the labels on the $x$-axis of your plot.
What can be done with such features, is you can create new features using the categorical variables, this however would be very problem specific and without additional details not much can be recommended. For example, in some cases using TF-IDF features may beneficial, or you could replace the categories with the conditional means of the target variable given the category (so called mean encoding or target encoding), etc. and treat them as continuous features.