Is there any mechanism for storing all the information of a probability distribution (discrete and/or continuous) into a single cell of a table? If so, how is this achieved and how might one go about making queries on these cells?
Your question is very vague. So only general hints can be provided.
I'd say there are two typical approaches for this (if I got your question right):
you can store some complex data into a single "cell" (how you call it) inside a database table. Easiest for this is to use
JSON encoding. So you have an array of values, encode that to a string and store that string. If you want to access the values again you query the string and decode it back into an array. Newer versions of MariaDB or MySQL offer an extension to access such values on sql level too, though access is pretty slow that way.
you use an additional table for the values and store only a reference in the cell. This actually is the typical and preferred approach. This is how the relational database model works. The advantage of this approach is that you can directly access each value separately in sql, that you can use mathematical operations like sums, averages and the like on sql level and that you are not limited in the amount of storage space like you are when using a single cell. Also you can filter the values, for example by date ranges or value boundaries.
In the end, taking all together, both approaches offer the same, though they require different handling of the data. The fist approach additionally requires some scripting language on the client side to handle encoding and decoding, but that typically is given anyway.
The second approach us considered cleaner and will be faster in most of the cases, except if you always access to whole set of values at all times. So a decision can only be made when knowing more specific details about the environment and goal of an implementation.