Where was this Staircase going to? | Gwulo: Old Hong Kong

Where was this Staircase going to?

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Where was this Staircase going to?

It is just next to West End Park Sub-station, 84A Robinson Road.

How come a staircase leads to a nullah?

I believe it was not a nullah long long ago.

There is an exit at Lyttelton Road with the same stone pillars, 

opposite to the school, next to the bus stop.