[susan53]

It's really closer to a non-defining clause, as it really just adds information. That's why I think that sounds a bit odd here - notice I've used which. It's a grey area. Again the problem is the lack of context. Compare it with.

The hotel has a swimming pool that's really big, and two others that are smaller.
Here the clauses are clearly defining as I'm distinguishing between them. Compare it with :
There are two types of camel. A camel that only has one hump is called a dromedary; the type that has two humps is called a bactrian. Here I seem to be classifying.

Quirk et al in A Grammar of Contemporary English point out though that relative clauses can refer either back to a) a definite person or thing - The man that took the money had red hair - in which case there's frequently a definite determiner, or b) forward - in which case the determiner is often indeterminate - A camel that only has one hump is called a dromedary.

In (a) you can take the relative clause out and the sentence remains comprehensible/correct - The man had red hair.
In (b) you can't do that : * A camel is called a dromedary.

This, I think, is where the distinction between definite and indefinite determiners is important. Not in the type of clause but whether the reference is backward (anaphoric) or forward (cataphoric).

That doesn't mean though that indefinite determiners are impossible in defining relative clauses with anaphoric reference :
Any book that you read will tell you the same thing
A girl that I know has just come into the room.

The sentences Any book will tell you the same thing / A girl has just come into the room are fine. It's a matter of frequency, not a rule - and as always, frequency depends on contexts.