Option B: 'In spite of' means 'without being affected by the particular fact mentioned'. It agrees in meaning with the given sentence:
His riches do not affect him, he is not happy even though he is rich.
Hence option B is correct.
Option A: 'Because of' expresses a cause or reason. One's riches cannot be the cause of one's unhappiness.
Option C: 'Owing to' also expresses cause.
Option D: 'In the event of' expresses a hypothetical condition. It states something that hasn't happened yet. But the given sentence here states a present action 'he is not happy'.
These options do not form a complete and meaningful sentence.
Hence, options A, C and D are wrong.