Funeral = a coffin / the coffin

Hi,

Here's my sentence (I am telling someone about a funeral I had to go):

"Of course I was sad. I found myself at a funeral, staring at a coffin. Who wouldn't be sad?"
OR
"Of course I was sad. I found myself at a funeral, staring at the coffin. Who wouldn't be sad?"

This is the explanation I understand:
a coffin = it's the fact that there was a coffin - any coffin - that made me sad. It could have been another coffin. Also, it's a way to introduce this noun.
the coffin = the emphasis is slightly different. A personal's funeral involves a coffin usually. It was that coffin. This is possible too because the context makes it logical.

So it depends on how I want to emphasize it here. Makes sense to you?