Context
You mention you need a plumber and your friend happens to be one.
Pues resulta que...
'Well it turns out that...' — resultar is the go-to verb for convenient coincidences in Spanish.
Conversational pivot — used to introduce a convenient coincidence or a relevant fact, often with mild surprise.
'Como sucede' is too literal and sounds like a documentary. The Spanish has a completely different feel.
Context
You mention you need a plumber and your friend happens to be one.
Pues resulta que...
'Well it turns out that...' — resultar is the go-to verb for convenient coincidences in Spanish.
Context
Someone asks if you've met the new boss and you have.
Pues mira, da la casualidad de que sí.
As it happens, yes — da la casualidad is the closest direct equivalent to 'as it happens.'
Context
Revealing you already knew the answer all along.
Casualmente, ya lo sabía.
Casualmente = coincidentally, as it happens — slightly formal but very natural.
Context
Bringing up a relevant fact at exactly the right moment.
Qué curioso que lo menciones.
'How curious that you mention it' — cues the relevant information with mild surprise.
Context
A serendipitous connection at a party.
Mira tú qué casualidad.
Well what a coincidence — warm, slightly amused. Very natural spoken Spanish.