I'd say it's a bad question. "Though" is correct if you assume that normally someone would stop working outside when it started to rain. However, if he was doing some work that could only be done in the rain, or was better to do in the rain, then "since" or 'because" would be fine.
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AngliholicI don't know what's wrong with the other two choices.It's not a grammar question. It's a question about meaning and common sense. You have to be sure you understand the meanings of since, because, and though, or you can't answer the question.