. . . . . . . . king of Scotland saw . . . . . . . . spider trying to climb up to . . . . . . . . ceiling of the cave.

In the given sentence, the noun phrase, 'king of Scotland' refers to a particular person as there can be only one king of Scotland. Hence, this phrase should be preceded by the definite article 'the'.
The word, 'spider' is a common noun. In the given sentence, it does not refer to any specific spider. Hence, an indefinite article ('a' or 'an') is to be used before this word. As the word, 'spider' starts with a consonant sound, the article 'a' is to be used before it.
The word cave is preceded by the definite article 'the'. Hence, we know that it refers to a specific cave. The ceiling of such a specific cave should also refer to a specific ceiling. Hence, the noun phrase, 'ceiling of the cave' should be preceded by the definite article, 'the'. Option A indicates this correctly and is the correct answer.