We investigate the absorption spectrum of a laser-driven V system in w
hich one of the upper levels is metastable. If the Rabi frequency of t
he laser driving the metastable transition is sufficiently small we fi
nd an extremely narrow peak in the stationary absorption spectrum of a
weak probe on the strong transition. We give analytical expressions a
pproximating the stationary absorption spectrum. The absorption spectr
um of a two-level system is investigated for the case where an upper l
imit for the time separation of successive emissions is given. The abs
orption spectrum then exhibits a delta-function-like peak and using th
is we then show that the origin of the narrow peak in the absorption s
pectrum can be traced back to electron shelving, i.e. to the existence
of light and dark periods in the resonance fluorescence emitted on th
e strong transition.