There are two frameworks (contexts here). If you take the time to work through the logic of the explanations below, you will see how this is handled by the logic of the English language. These uses depend on context. Not single utterances. I would argue (I do actually think) that without more than a single sentence, one cannot explain how the ‘a’ determiner versus the ‘the’ determiner actually work together in cases such as these.
The reason ELLers get into a bind with this issue is because some questions do not supply enough context to make an explanation possible. So, here we go...
The ‘a’ determiner for a non-specific case (AN arrest) and the ‘the’ determiner when that first time use becomes specific in the same text or speech utterance.
A plural noun instead of an ‘a’ determiner (arrests)
Individual times take an a determiner.
In 1. Now, let's say, the person was arrested a first time and a second time. OK, he was arrested twice. Now, the second time he was arrested, he was not charged.
In 2. If he was arrested a second time, if you want to now go on and refer to that second time, you would use "the". It has become specific.
2) He was arrested five times. “The second time was a nightmare.” The second time is now specific as it refers to one of the five times.
Summary: Both cases refer to non-specific situations. The "the" is then used to make them specific within the same text or speech utterance.
That's how this works.