This is a subtle distinction in this instance.
In English, generally, you use the article "the" when referring to a unique entity in the world, one that is typically already known to the audience.
The prime minister is having a bad day.
If you're in a country with a prime minister, it's assumed that the prime minister is the one who leads your country. There is only one of them, and they are already known. In America (which has a president) you could not say that sentence without first mentioning what country the PM is from or which prime minister you mean.
In Britain, the prime minister is having a bad day.
We met the British prime minister. The prime minister was having a bad day.
But what about your example?
Although theoretically there can only be one second example, there could actually be more than one.
Second examples were sent to London and Paris.
As long as the animal sent to London is the second of that animal in London, and the animal sent to Paris is the second of that animal in Paris, there can be two second examples.
If you use "the second example", you are then saying that this is the one and only of that animal that is considered a second example in the context of this story. If you say "a second example", you are saying there could be other second examples in the context of the story, like a second example sent elsewhere.