"[will] likely" vs. "[will] probably" in AmEng usage

In examples 2-4, likely is a predicate adjective, appearing with auxiliary be: is likely, are(n't) likely.
Probably is always an adverb, so it can't substitute for a predicate adjective.

That leaves 1, 5, and 6, where likely can substitute for probably. Both are adverbs, and both occur after the first auxiliary verb (will likely, have likely), which is normal and common.

However, an auxiliary verb is not necessary; likely occurs with simple verbs as well:

• He likely slipped on the steps and fell.
• This likely has nothing to do with it, but ...

In effect, in American English, likely is a 2-syllable adverb complementing a 3-syllable probably.

They could be in a round-about way. Using your examples-

The traffic is terrible so I'll probably be late this morning.

The traffic is terrible so I'm likely to be late this morning.

Climate change is likely to affect us all by the end of the decade.

Climate change will probably affect us all by the end of the decade.

I'll call them if you like, but they aren't likely to be in.

I'll call them if you like, but they probably won't be in.

The concert tickets are likely to sell out very quickly.

The concert tickets will probably sell out very quickly.

I'll probably find out if I've passed or not by the end of the day.

I'm likely to find out if I've passed or not by the end of the day.

You've probably heard this joke before, but I'll tell you anyway.

You're likely to have heard this joke before, but I'll tell you anyway.

Not all of these work well, but all are understandable and make sense.

"You just walked into the wrong likelihood."

A diverse question, an even more varied problem, let's start with basics.

Introducing chance to make it whole. (http://www.thefreedictionary.com/chance - definition(s) too long to list.)

Possible and certain are kind of an inseparable pair, when talking about future events.

• Certainty: Improbable to error, infallible, concrete, perfect knowledge, or the mental state of no doubt. Objectively defined, certainty is total continuity and validity of all foundational inquiry, to the highest degree of precision. Something is certain only if no skepticism can occur.

  https://en.wikipedia.org/wiki/Certainty

  https://en.wikipedia.org/wiki/Certainty_effect

• Certain:

  Google- Able to be firmly relied on to happen or be the case.

  CDO - http://dictionary.cambridge.org/dictionary/english/certain

Modal verbs demonstrate we believe something is certain, probable or possible. Ignoring plausible, as that is the sound of truthiness instead.

The modal verbs, two distinct groups:

• Classic: Can, could, may, might, shall, should, will, and would.

  The observed, inferred Chances.

• Conventionally common: Going to, need to, must, (+will) have to, etc.

  The passively suffered chances, action-inducing, no guesswork or observation needed. These can also be combined with likely, certainly, etc.

Possible/possibility, Impossible/Impossibility: An option, can happen, regardless of probability/likelihood. There is a chance for it.

• Could indicates present or past(of can).
• Then: Could, might, may fall here. Have form indicates now or past.
• Can, cannot are the general statements.

Probable/probability, Improbable/improbability:

Acting on possible(!). Probable is probability with some certainty or chance in the "equation". Improbable is doubt of probability, same as before.

• Must shows a forcing condition to be, without a doubt, be true, and action is required unconditionally now. Must have (something continuous) is used for near past, and normal past.
• Should is a suggestion - something will be(uncertain, but probable), or is true. Should have, again is a past indicator.
• Shall indicates future, akin to will. (http://dictionary.cambridge.org/dictionary/english/shall)

Likely/likelihood, Unlikely/Unlikelihood:

Likely: http://www.merriam-webster.com/dictionary/likely, https://en.wiktionary.org/wiki/likely

As a wiki is open to edit, and merriam-webster is less prone to erroneous edits or NNE tinkering, I'm going to rely on the first link's definitions, particularly the most bare, simple definition, which is more common in written and spoken English.

• (some adjective) likely, needing a "crutch" to be valid in a sentence.
• very/somewhat/highly (un)likely to rain

Likelihood:

the state or fact of something's being likely; probability.(http://www.merriam-webster.com/dictionary/likelihood)

In conclusion:

• Possible is an observed option, a near, or not so close future event.

  This has a "pool"(kiddie pool) of percentage of happening - the likelihood, chance. Certainty, Likelihood, possibility pertain to the pool containing something(it exists).

  • Probable is about the percentage of that - A perceived(more than meets the eye?) possibility, fallible, which is less than, but mostly certain.

  • Likely - A possibility is playing in the pool.

  • Chance is a (mostly, or mostly used as) binary outcome observation of possibility. Chancy is very uncommon just because of Chance's nature.

  • Likely sits inbetween, with both being an uncertain qualifier, and a scale of probability percentage indicator. The most versatile.

  • Certain is a concrete binary outcome observation of probability.

Points taken from British Council's English learning article(http://learnenglish.britishcouncil.org/en/english-grammar/verbs/modal-verbs/certain-probable-or-possible)

Then a very good explanation from Robert B. Mercer here: http://www.usingenglish.com/forum/threads/14222-likely-probably-possibly

A good question on ELL about this: https://ell.stackexchange.com/questions/21191/in-simple-words-what-is-the-difference-between-possible-and-probable

Finally:

AmEng dislikes ambiguity in certainty, so would more than likely use probably, or possibly than likely. Likely is more "scientific".

Not mentioning the linguistic ambiguity likely induces in a sentence, as per above explanation. As far as alternates go, unlike synonyms, yes. One could use likely, but probably wouldn't. (I better go into hiding now.)

Likely is more like "there's a good chance something is going to happen" Probably means more like "it should happen and 90% + will happen"