The Vera C. Rubin Observatory, previously known as the Large Synoptic Survey Telescope (LSST), is expected to alert on up to ten million transient astronomical events each night of observation. This high volume of alerts calls for a system that can determine the type of transient upon initial discovery so immediate action may be taken to follow up on notable events before they fade away. We propose a probabilistic model to predict the relative likelihood across a range of transient events using host-galaxy features, which would allow for the immediate classification of transients when first detected by the Rubin Observatory. We design our model with the intention of applicability to the Rubin Observatory by ensuring the transient classes in our dataset are properly distributed over ranges of redshift with respect to expected distributions from the Rubin Observatory, using only readily available photometric data, and by either excluding transient class frequency or using expected rates. We develop a multiclass classifier using unique kernel density estimates per class in order to estimate the underlying distribution of galaxies per transient class. Initial results have indicated that we can distinguish SNe Ia, SN II, tidal disruption events, and gamma-ray bursts at significant rates of purity, which indicates that we may expect to have immediate follow-up on a portion of these events when alerted upon by the Rubin Observatory.