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I know the following two sentences give implication that "not expecting me to
understand (it)" but I have a feeling that they give different nuances that I
just can't put my finger on:

> それは分{わ}かる **わけがない** でしょう。 _sore wa wakaru **wake ga nai** deshou._
>
> それは分{わ}かる **はずがない** でしょう。 _sore wa wakaru **hazu ga nai** deshou._

Would someone explain what is the difference of the two sentences, and also
how to choose between using はず and わけ?
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word-choice formal-nouns
What is the difference between 「はずがない」 and 「わけがない」?
I believe the difference emphasis.

それは分かるわけがないでしょう。 sore ha wakaru wake ga nai deshou. - I'd read this as
わかりようがない

それは分かるはずがないでしょう。 sore ha wakaru hazu ga nai deshou. - and this as he doesn't
have a chance to understand this. This is the stronger of the two.
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I would expect the わけ version to be stronger. If you look at the meaning of わけ
and はず in isolation, わけ means 'reason' - eg, in the pattern of
「どうしてそうなったの？／〜〜〜〜したわけ。」 はず however expresses an expectation - 「こうなるはず。」 Thus,
if you use わけ, you imply that you can't understand why such a situation would
happen; with はず, you imply that you simply wouldn't _expect_ such a situation
to happen (or, retrospectively, you express that you, previously, strongly
expected it not to happen)
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I'd translate them as follows:

> 分かるわけがないでしょう。 _Wakaru wake ga nai deshō._

"There's no way _(he)_ can understand this." or " _(He)_ surely doesn't
understand this."

> 分かるはずがないでしょう。 _Wakaru hazu ga nai deshō._

"I don't think _(he)_ understands this."

はず is more of a personal inkling, while わけ is more of an
objective/direct/strong statement. Depending on how it's meant わけ can be used
insultingly:

> 出来るわけないだろう。 _Dekiru wake nai darō._

" _(You)_ can't _(are unable to)_ do that!" or "Are _(you)_ crazy to think
_(you)_ can do that?"

> 出来るはずはないけど… _Dekiru hazu wa nai kedo…_

" _(I)_ don't think _(you)_ can do it, but... _(maybe I'm wrong about that)_ "

More, negated examples:

> 出来ないわけがないでしょう。 _Dekinai wake ga nai deshō._

"It's not impossible, right?" or "It _should_ be possible, right?"

> 出来ないはずはないですが、今は難しいです。 _Dekinai hazu wa nai desu ga, ima wa muzukashii desu._

"I don't think it's impossible, but it's very difficult right now."
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disclaimer: not a native speaker

I think 'wake' implies that things happened as expected, where as 'hazu'
implies that what happened is not what was expected.

Or, 'wake' is a bit more neutral, a "matter of fact", where as 'hazu' is more
of a personal opinion/subjective kind of thing.

This is how I would understand the difference:

> それは分かるわけがないでしょう。 sore ha wakaru wake ga nai deshou.

You're not meant to understand this .. it's normal.

> それは分かるはずがないでしょう。 sore ha wakaru hazu ga nai deshou.

I see no reason you could understand this .. so what's going on?
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Wake is a reason or cause; hazu is an expectation. They can be used in the
same context, but still have a different sense.

分かるわけない！ "How would you understand?!" (there's no reason to think you would
get this) わかるはずはない "He shouldn't understand" (I expect that he doesn't).
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Disclaimer: Not a native speaker.

Based on how I hear it being used and also from the goo dictionary usage
explanation, I don't think the difference is that much (as to be worried about
when to use which).

Even if the dictionary gives different example sentences for the usage:

[使い方]

〔わけがない〕▽朝寝坊のあなたが、朝五時に起きられるわけがない

〔はずがない〕▽小さい子供が四人もいるのだから、家の中がきれいなはずがないでしょ

They club it together in the "proper use" section

[使い分け]
【１】「わけがない」「はずがない」は、…する理由がない、…する道理がない、の意味で、ある事態の起こる可能性が全くないことを表わす。「わけはない」「はずもない」などの形もある。

To me, its as simple as:

わかるはずがない： (I wasn't in town,so)How would I know?(what happened to him)

わかるわけがない： (I wan't in town,so)No way of knowing(what happened to him)
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