Your generative process is still rather ambiguous. What I understand is that the variable S is a prior unknown, and is assumed to be sampled from a Uniform(0,1). Then you get 20 samples of another variable K, which you would treat as your observed data.
How does S relate to K?
This question is the key to fully set up your generative process. For example, let’s imagine that S determines the standard deviation of K, and that the mean is always 1.3. In this case you would write down your model as
with pm.Model():
S = pm.Uniform('S', 0, 1)
K = pm.Normal('K', mu=1.3, sigma=S, observed=your_observed_data)
# And finally you infer the posterior of S doing this
trace = pm.sample()
pm.traceplot(trace)
pm.plot_posterior(trace)
This is an interpretation from what you wrote of your case, but the key link that you still need to write down is how does S condition the values observed in K? I honestly, cannot help you with that because it depends entirely on your experiment setup. Once you sort that out, you should be able to write down your model and use sample to infer S's posterior