So i looked through this research. https://www.cambridge.org/core/journals/american-political-science-review/article/abs/war-and-the-fate-of-regimes-a-comparative-analysis/88056B8C9BE0413DB349086653B58520

The research is rather limited because it looks at violent regime changes (aka revolutions). There are more way a regime change can happen so all the probabilities need to be adjusted. 

Here is some data relevant for the question. For regimes that initiated wars and lost them the regime change by violence within 3 years is 60-80%. For an initiator that won the probability is 20-35%. Because there are multiple other ways to change the regime i think these probabilities need to be doubled, and since we are looking only at 1 year frame, then I would divide them by 3.

So we have 40-55% in case of Russian loss and 13-23% in case of win.

Assuming there is a 40% chance of win - then the probability of regime change is 35%.

I infer a base rate of regime change of about 7% per year, which would apply until the conflict is resolved.

Assuming a 30% quick resolution then the regime change probability ends up being around 15%.

I will have to adjust upward this probability if a resolution to the war comes closer or if the win of Ukraine becomes more apparent.