Do diagram Markov categories have conditionals?

I’m working on using Markov categories with conditionals to represent nondeterministic behaviours. The following question popped up: given a Markov category with conditionals C, and a small category I, is it true that the diagram category Fun(I, C), with pointwise operations, has conditionals ?
I suspect it doesn’t hold in general.

The more specific example I am interested in is that of Fun_{cart}(Arity, BorelStoch), the category of strict cartesian functors from the category of arities (dual to that of finite sets/free cartesian in one generator) to the Markov category of standard Borel spaces and measurable Markov kernels.
It would be nice if it had conditionals, however I strongly suspect it does not…

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I’ll try to ping @mromang08 to answer this one.

Update: I am now convinced the example of Fun_{cart}(Arity, BorelStoch) is not “the correct one”.

A more interesting (to me, right now) Markov category is that of Quasi-Borel spaces: there is an affine (strong) commutative monad on QBS (for instance, by Theorem 21 and Proposition 22 in [1701.02547] A Convenient Category for Higher-Order Probability Theory), which then yields a Markov category. It would be really nice if this one, or a large chunk of it (larger than BorelStoch) had well-behaved conditional products.