As adjectives, they have the same meaning eg What is the likely result? What is the probable result?'
'Likely' is used much more frequently than 'probable' . 'Probable' is rather more formal, and isn't appropriate for all situations .'Likely' is also more flexible grammatically, because you can use it in constructions such as:
Is it likely to rain?
He is likely to be late.
You couldn't use 'probable' with this construction.
In American English, 'likely' is used as an adverb. (eg He will likely be late). This construction isn't used in standard British English.