Fate may be defined as an event or happenstance that unavoidably befalls, or occurs to, a person. The major instances of the presence of fate in "An Astrologer's Day" are the lighting the astrologer uses; the cheroot the customer lights; the recognizability of their faces. Narayan spends a great deal of time in the pages of his story describing the setting and the astrologer. Part of the reason for this is so that the reader recognizes the role of fate regarding the lighting, cheroot, and the astrologer's face.
His face is described as being resplendent with "sacred ash and vermilion" and topped by a "saffron-coloured turban" wound around his head. In between these were his sparkling, powerful eyes and his long heavy dark whiskers:
The power of his eyes was considerably enhanced by their position--placed as they were between the painted forehead and the dark whiskers which streamed down his cheeks : even a half-wit's eyes would sparkle in such a setting.
It is this way of presenting himself--and the change to the quality of his eyes, with their "sharp abnormal gleam"--that made his face unrecognizable. In this way fate intervenes to shape events and to allow the astrologer to remain a stranger in the presence of the man whom he had wronged so many years ago.
In contrast, it is the lighting of the customer's cheroot (i.e., open-ended cigar) "by the matchlight" that illuminates the customer's face allowing the astrologer to recognize him. Narayan describes the lights of the market with specific detail and makes it clear that the astrologer is bathed in shadow touched only by ambient light. By these features, fate intervenes to shape events through the physical lighting and the lighting of the cheroot to allow the customer to be recognized by the hidden astrologer.