はず isn't a guess — it's the sound of things clicking into place

Where the picture shows up in はず

1. 1

   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.

2. 2

   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.

3. 3

   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.

   はずなんですが flags the gap: this is the calculation, and reality disagrees.

4. 4

   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.

   Nouns and な-adjectives need の: 休みのはず.

5. 5

   nothing meshes

   そんなはずはありません。

   sonna hazu wa arimasen

   That can't be right.

   かもしれない leaves a possibility open; はず closes it with evidence.