The circumstellar ammonia (NH$_3$) chemistry in evolved stars is poorly understood. Previous observations and modelling showed that NH$_3$ abundance in oxygen-rich stars is several orders of magnitude above that predicted by equilibrium chemistry. In this article, we characterise the spatial distribution and excitation of NH$_3$ in the O-rich circumstellar envelopes (CSEs) of four diverse targets: IK Tau, VY CMa, OH 231.8+4.2, and IRC +10420 with multi-wavelength observations. We observed the 1.3-cm inversion line emission with the Very Large Array (VLA) and submillimetre rotational line emission with the Heterodyne Instrument for the Far-Infrared (HIFI) aboard Herschel from all four targets. For IK Tau and VY CMa, we observed the rovibrational absorption lines in the $ u_2$ band near 10.5 $mu$m with the Texas Echelon Cross Echelle Spectrograph (TEXES) at the NASA Infrared Telescope Facility (IRTF). We also attempted to search for the rotational transition within the $v_2=1$ state near 2 mm with the IRAM 30m Telescope towards IK Tau. Non-LTE radiative transfer modelling, including radiative pumping to the vibrational state, was carried out to derive the radial distribution of NH$_3$ in these CSEs. Our modelling shows that the NH$_3$ abundance relative to molecular hydrogen is generally of the order of $10^{-7}$, which is a few times lower than previous estimates that were made without considering radiative pumping and is at least 10 times higher than that in the C-rich CSE of IRC +10216. Incidentally, we also derived a new period of IK Tau from its $V$-band light curve. NH$_3$ is again detected in very high abundance in O-rich CSEs. Its emission mainly arises from localised spatial-kinematic structures that are probably denser than the ambient gas. Circumstellar shocks in the accelerated wind may contribute to the production of NH$_3$. (Abridged abstract)
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