Hello Soomin! "the' and "a" are both determiners showing more about a noun - a specific thing or any random thing. In this verse in the Bible, "the rooster" is used instead of "a rooster" because the rooster being spoken about is a specific rooster that crows every morning (which is expected and could even be a way of keeping track of time). The emphasis here is when it crows and that the betrayal will happen before this usual occurrence - the crowing of the rooster. If "a rooster " was used then it would mean that any random rooster is being spoken about and the timing of the rooster crowing may not be as precise. I hope this helps!

My own Bible calls it a "cock" rather than a "rooster", which makes it a bit clearer. "Cockcrow" means dawn. As people have described below, "the" means a general case, which means the cock which crows at cockcrow. I hope that was understandable!

Have a look at the link below. This is from it:. "The with everyday things We use the with things that we know as part of our daily lives. The does not refer to particular things in this context. I don’t buy the newspaper these days. It’s free on the Internet. (newspapers in general) They always take the train. (trains in general) " https://dictionary.cambridge.org/grammar/british-grammar/a-an-and-the

"The" rooster = Peter would have known exactly which rooster He was talking about (therefore it wasn't just any rooster) It could have been visible to Peter, ie just nearby to where they were talking. "A" rooster = it could have been any rooster, nobody would have known which rooster He was talking about. "The" dog will bark soon (Everyone knows exactly what dog is being spoken about) "A" dog will bark soon (nobody knows what dog - it could be any dog)