Geographical question: where is the most likely precipitation under high pressure?

It depends on the nature of high pressure.

If it is cold high pressure, precipitation is easy to appear at the bottom of cold high pressure. This is because high pressure extends to low latitudes, and cold air from the south often meets warm and humid airflow at low latitudes to produce precipitation.

If it is warm and high pressure, precipitation is easy to occur at the back of the high pressure, because the back of the high pressure brings a lot of warm and humid airflow from low latitude, which is easy to occur.