Article before "Umbrella"

Hi, A question: let's say someone enters a room. There's an umbrella in the corner. I am sitting at a desk. I say to the person:

"If you fill out this card, you will win AN umbrella."

"If you fill out this card, you will win THE umbrella."

Either is correct, right?

"An umbrella" is ambiguity (which one? maybe not the one in the corner but some other one) but correct.

"The umbrella" is correct also and is better if I point at the umbrella in the corner.

And I think I can also use a demonstrative (this/that umbrella).

Thanks.