Visa Refusal Request PREVIOUS – United Kingdom

I am planning to apply for a British visa, but last October my Schengen visa from Greece was rejected, saying:

1- The justification for the purpose and conditions of the intended stay has not been provided.
2- The information provided regarding the justification of the purpose and conditions of the intended stay was not reliable.

Basically, I feel that the problem of my application for Greece was that I did not provide a cover letter explaining the purpose of the visit.
Brief history: I am single and worked for a bank for 4 years. Living with my family in UAE for 8 years. I am hardly traveling, but my employer awarded me the travel award last year. This trip must now be used in the same way.

So, please advise how do I address the question below in the UK visa application.

"Have you ever refused a visa for a country other than the UK and explain nicely what happened?"