Difference between Unlikely and Inconceivable

UNLIKELY vs INCONCEIVABLE: NOUN

Totally unlikely
Impossible to comprehend or grasp fully.
So unlikely or surprising as to have been thought impossible; unbelievable.
Not conceivable; incapable of being conceived by the mind; not explicable by the human intellect, or by any known principles or agencies; incomprehensible.
Unable to be conceived, unbelievable

Such as cannot be reasonably expected; improbable: as, an unlikely event.
Not holding out a prospect of success or of a desired result; likely to fail; unpromising.
Not calculated to inspire liking or affection; not likable or lovable.
In an unlikely manner; with no or little likelihood; improbably.

Incredible; not to be imagined as believed in by any man, as the supposition of an event undetermined by a cause.
Capable of being conceived only by a negative or relaive notion, such as the idea of infinity.
Unimaginable to a particular person from novelty, as the idea that parallel straight lines meet at infinity.
Unimaginable by man on account of an inseparable association, although not perhaps involving any contradiction nor even physically impossible, as the perception of color without extension.
Unacceptable to the mind because involving a violation of laws believed to be well established by positive evidence, as a perpetual motion.
An expression which conveys no conception whatever, but is mere gibberish, is not called inconceivable, but unintelligible. The word inconceivable (see also unconceivable) is used in the following senses in philosophy: Involving a contradiction in terms, such as the idea of a non-existent being.
Incapable of being conceived, or realized in the imagination; incredible; inexplicable.

Impossible, Reluctant, Plausible, Inconceivable, Doubtful, Likely, Outside, Remote, Last, Unbelievable, Supposed, Unconvincing, Farfetched, Implausible, Improbable

Unbelievable, Unfeasible, Shocking, Unconscionable, Unacceptable, Untenable, Absurd, Unheard, Unlikely, Incomprehensible, Conceivable, Out of the question, Impossible, Unimaginable, Unthinkable

Impossible, Reluctant, Plausible, Inconceivable, Doubtful, Likely, Outside, Remote, Last, Unbelievable, Supposed, Unconvincing, Farfetched, Implausible, Improbable

Unbelievable, Unfeasible, Shocking, Unconscionable, Unacceptable, Untenable, Absurd, Unheard, Unlikely, Incomprehensible, Conceivable, Out of the question, Impossible, Unimaginable, Unthinkable

Obviously, in my case it is EXTREMELY unlikely.
John Mark might not be unlikely at all.
Spain but I think this one is unlikely.
Discountable effects are those extremely unlikely to occur.
NBA comeback may seem unlikely at this point.
Russia investigation even though his election seemed unlikely.
It indicates the null hypothesis is very unlikely.
Just as people who borrow murder mysteries are unlikely to be murderers, so those seeking information about terrorism are unlikely to be terrorists.
When looking for solutions to problems they are unlikely to arbitrarily rule out any possibilities, even if they may seem unlikely to others.
Responses can be: very likely, somewhat likely, neither likely or unlikely, somewhat unlikely and very unlikely.