Difference between Unlikely and Rare

UNLIKELY vs RARE: NOUN

(of meat) cooked a short time; still red inside
Marked by an uncommon quality; especially superlative or extreme of its kind
Having low density
Not widely distributed
Not widely known; especially valued for its uncommonness
Recurring only at long intervals
Infrequently occurring; uncommon.
Excellent; extraordinary.
Thin in density; rarefied.
Cooked just a short time so as to retain juice and redness.
Thin; of low density
Very uncommon; scarce.
Nearly raw; partially cooked; not thoroughly cooked; underdone.
Not frequent; seldom met with or occurring; unusual.
Of an uncommon nature; unusually excellent; valuable to a degree seldom found.
Thinly scattered; dispersed.
Characterized by wide separation of parts; of loose texture; not thick or dense; thin.
Cooked very lightly, so the meat is still red (in the case of steak or beef in the general sense).

In an unlikely manner; with no or little likelihood; improbably.
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.

Early.
Not thoroughly cooked; partly cooked; underdone: applied to meat: as, rare beef; a rare chop.
A dialectal form of rear.
An obsolete form of roar.
Thin; porous; not dense; of slight consistence; rarefied; having relatively little matter in a given volume: as, a rare substance; the rare atmosphere of high mountains.
Thinly scattered; coming or occurring at wide intervals; sparse; dispersed.
Very uncommon or infrequent; seldom occurring or to be found; hardly ever met with.
Hence Remarkable from uncommonness; especially, uncommonly good, excellent, valuable, fine, or the like; of an excellence seldom met with.
Synonyms Rare, Scarce, infrequent, unusual. Rare implies that only few of the kind exist: as, perfect diamonds are rare. Scarce properly implies a previous or usual condition of greater abundance. Rare, means that there are much fewer of a kind to be found than may be found where scarce would apply.
Singular, extraordinary, incomparable, choice.
(of meat) cooked a short time
Marked by an uncommon quality
Not widely known
Still red inside

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

Seldom, Remarkable, Atypical, Rarely, Unheard, Unusual, Rarity, Thin, Raw, Rarefied, Scarce, Rarified, Extraordinary, Infrequent, Uncommon

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

Seldom, Remarkable, Atypical, Rarely, Unheard, Unusual, Rarity, Thin, Raw, Rarefied, Scarce, Rarified, Extraordinary, Infrequent, Uncommon

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.

They exceeded expectations, which is rare these days.
Practical Methods for Sampling Rare and Mobile Populations.
This is an optional step, and is generally only used if your card is an ultra rare, a rare holo or a promo.
Rare Fish Tracker helps you keep track of the rare fish you have caught in your pursuit of fishing achievements.
Bipolar disorder is extremely rare in children, and although it can begin in adolescence, this is also rare.
The Drum Broker has launched Rare Rhythm Paints, a sample pack featuirng a collection of original and rare percussion samples by Dougles Fitch.
Rare birds: A few rare bird species were mapped using data supplied by MD DNR from their Ecologically Significant Areas database.
Nicely rare or medium rare, they are moved to rest and the pan deglazed with red wine.
Rare Coin Investments for decades has consistently offered better quality in rare coins.
Other symptoms may be rare or very rare.