The word among these three that connects with the other two is liable, which means responsible by law, legally answerable, and subject by law to. The word has a clear connotation of the law and legal matters. Yet when expressing in speech the idea of probability of occurrence, many use the word as a substitute for likely, even if no connotation of the law is intended.
Precise writers will use likely to express conditions of probability and liable to express subjugation to the law. Thus, these writers would revise the sentence in the cropped graphic above to read as follows:
You’ll likely write better when you understand libel and liable. Using that precision of language promotes your own reputation as a more effective writer who can present desired messages to your audience more effectively. And that more effectively represents both you and your brands to that same audience.