Likely simply means probable. Liable means legally or financially responsible, or prone to something unwanted. Memory hook: liable is tied to liability, so if blame or bad outcomes are involved, liable may fit; otherwise use likely.
The core difference
Likely means probable, while liable means responsible in law or money, or prone to something unwelcome.
- likely — probable: It's likely to rain later.
- liable — responsible: The landlord could be held liable for the faulty wiring.
- liable — prone to something unwanted: This old ladder is liable to collapse under too much weight.
How to tell them apart
Use likely for ordinary chances, good or bad: She's the most likely candidate for the job. It can also be an adverb, as in He'll likely be late again.
The mix-up arises because liable to can also mean probable, but it is used mainly for unwelcome outcomes. Nobody would say a pleasant surprise is liable to happen. When in doubt, likely is the safer, neutral choice, and liable is best kept for responsibility or risk.