Bayesian inference and intractable distributions

Hi to all, I'm struggling with a question on my personal studies about bayesian inference, mainly on dinamical system, Kalman and Particle filters. In the latter, we use sampling tecniques to find the state x(t) given observatio up to time t, i.e. we want to find p(x(t)|y(1:t)). We use sampling techqniques because we don't know, for example, the normalizing constant of the bayes formula. For example, in the formulation P(A|B)=P(B|A)P(A)/P(B), I've read that typically we cannot compute P(B), which involves an integral. What I can't understand is why we can't calculate this integral and an example in which, effectively, we can't. I've read that techniques like MCMC have been developed for this purpose but I can't understand when the problem can occur. Thanks in advance!