Suutari huomasi kengän kantapään olevan rikki ja toisessa kengässä olevan pienen reiän.

Finnish has no articles, so it does not have separate words for the and a/an.

That means:

• Suutari can mean the cobbler or a cobbler
• pienen reiän can mean a small hole or, in some contexts, the small hole

You understand which one is meant from the context, not from an article.

The basic phrase is:

• kenkä = shoe
• kengän = of the shoe
• kantapää = heel

So kengän kantapää means the heel of the shoe.

In the sentence, it becomes kengän kantapään, because the whole phrase is inside a construction where that noun phrase appears in the genitive:

• kengän = of the shoe
• kantapään = the heel, in genitive form

So the structure is roughly:

• kengän kantapään olevan rikki
• the heel of the shoe being broken
• more naturally: that the heel of the shoe was broken

After verbs like huomata (to notice), Finnish often uses a participial construction instead of an että clause.

So:

• Suutari huomasi kengän kantapään olevan rikki means the same as
• Suutari huomasi, että kengän kantapää oli rikki

In simpler English:

• The cobbler noticed that the heel of the shoe was broken.

So olevan is part of a more compact Finnish structure meaning that something is/was.

Because in this kind of Finnish construction, olevan does not mean present time in the same simple way that English is does.

Here olevan shows a state that was true at the time of noticing. So even though the main verb is past tense, olevan is still normal.

Compare:

• huomasi hänen olevan väsynyt = noticed that he was tired
• luulin hänen olevan kotona = I thought he was at home

If you wanted to show that something had already been the case earlier, Finnish can use olleen instead.

Rikki is an indeclinable state word meaning broken.

It often appears with verbs like:

• olla rikki = to be broken
• mennä rikki = to break
• saada rikki = to break something

It does not behave like a normal adjective that agrees in number or case. For example:

• Kenkä on rikki. = The shoe is broken.
• Kengät ovat rikki. = The shoes are broken.

So rikki stays rikki.

Because toisessa kengässä means in the other shoe.

Breaking it down:

• toinen = other / second
• toisessa = in the other / in the second
• kengässä = in the shoe

The ending -ssa/-ssä is the inessive case, which usually means in.

So:

• toisessa kengässä = in the other shoe

Since a pair has two shoes, toinen very naturally means the other one of the two here.

Because the sentence is talking about one shoe at a time:

• one shoe had a broken heel
• the other shoe had a small hole

So Finnish treats each shoe individually:

• kengän kantapää = the heel of one shoe
• toisessa kengässä = in the other shoe

If it were talking about shoes in general or both shoes together, plural might be used instead.

Here pienen reiän is the object of huomasi.

With a singular, countable, complete object in an affirmative sentence, Finnish often uses the total object, which in the singular usually looks like the genitive:

• reikä → reiän
• pieni → pienen to agree with it

So:

• huomasi pienen reiän = noticed a small hole

If the sentence were negative, you would normally get the partitive instead:

• ei huomannut pientä reikää = did not notice a small hole

This olevan is modifying reiän.

So the phrase means literally:

• the small hole being in the other shoe

More natural English:

• the small hole in the other shoe
• or the small hole that was in the other shoe

So in the second half, olevan works like a compact relative clause.

You can compare:

• toisessa kengässä oleva pieni reikä = a small hole that is in the other shoe
• toisessa kengässä olevan pienen reiän = the same phrase, but in object form inside this sentence

It is grammatical and natural, but it is fairly compact and a bit more written-style than what many learners first meet.

A simpler version would be:

• Suutari huomasi, että kengän kantapää oli rikki ja että toisessa kengässä oli pieni reikä.

Or often in everyday Finnish:

• Suutari huomasi, että kengän kantapää oli rikki ja toisessa kengässä oli pieni reikä.

Those versions are easier because they use ordinary finite verbs:

• oli rikki
• oli pieni reikä

instead of the more compressed olevan structures.

Not quite.

The first half is more clearly a clause-like structure:

• kengän kantapään olevan rikki
• that the heel of the shoe was broken

The second half is more like an object noun phrase with a participial modifier:

• toisessa kengässä olevan pienen reiän
• the small hole that was in the other shoe

So the sentence mixes two compact structures after huomasi:

1. noticing that something was broken
2. noticing a hole located in the other shoe

That is one reason the sentence can feel dense to an English-speaking learner.