Replace column string values with multi if conditions in pandas

I need help to replace values in a column based on conditions of another column. I want to replace "pe60" with "pe61" in the "level_2" column if "pe60" is in the "level_2" column and "b" is in the "level_1" column. I want to do the same but replace "pe70" with "pe71" if "pe70" is in the "level_2" column and "b" is in the "level_1" column.

My desired solution is as follows:

data_sol = {'Name': ['Tom', 'nick', 'krish', 'jack','bob'],
        'level_1': ['a', 'b', 'a', 'b','a'],
        'level_2': ['pe60', 'pe71', 'pe71', 'pe61','pe60'],
        'level_3': [-2, -1, 4, 6,-4],
        }

df_solution = pd.DataFrame(data_sol)
print(df_solution)

How can I solve my problem?