はず
hazu
はず isn't a guess — it's the sound of things clicking into place
The picture Two gear teeth locking together. Line up what you already know and it can only land here. はず closes the fit with evidence; かもしれない leaves that same fit open by a finger's width.
Where the picture shows up in はず
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meshing with a timetable
9時の電車だから、もう着いているはずです。
ku-ji no densha da kara, mō tsuite iru hazu desu
It's the nine o'clock train, so he should be there by now.
A gear stamped '9 o'clock train' meshing with one stamped 'arrived', the two turning together.
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meshing with a process
昨日送ったので、今日届くはずです。
kinō okutta node, kyō todoku hazu desu
I sent it yesterday, so it should arrive today.
The parcel you posted yesterday rides the delivery gear round and drops neatly into today's slot.
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it should mesh, but doesn't
あれ、鍵はここにあるはずなんですが。
are, kagi wa koko ni aru hazu na n desu ga
Odd — the key is supposed to be right here.
The one notch where the key belongs sits empty, and the gear spins free.
はずなんですが flags the gap: this is the calculation, and reality disagrees.
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meshing with a noun
田中さんは今日休みのはずです。
tanaka-san wa kyō yasumi no hazu desu
Tanaka should be off today.
The name tag 'Tanaka' slotting into the 'day off' notch on the roster.
Nouns and な-adjectives need の: 休みのはず.
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nothing meshes
そんなはずはありません。
sonna hazu wa arimasen
That can't be right.
A gear pushed in that fits no notch at all and springs straight back out.
かもしれない leaves a possibility open; はず closes it with evidence.
All of it in one picture
はず is not five meanings but one pair of gears. Mesh it with the timetable and it becomes 'he should be there by now'; mesh it with the delivery process and it becomes 'it should arrive today'. When the notch that ought to be filled sits empty you get はずなんですが, and when a name slots into the roster you get 休みのはず, with の in front. When nothing meshes at all, そんなはずはありません. So every time you meet はず, just ask what is meshing with what.