I'm even not sure whether also non-0-fee TAs were/are forgotten which were/are totally valid.
At least it would be very helpful to have a probability whether a given TA will be included into the blockchain.
http://bitcoinfees.21.co/ seems to be of no help to this last question, isn't it?
As far as I know there are no websites that show probability calculation, and you can't calculate this based on a single node (i.e. your node). Different nodes have different rules. When it comes to zero confirmation transactions you can see that the delay is estimated between 15-Inf amount of blocks. It is like that for a reason.
If your node has a very large amount of the available TX you can use it to make a good guess though. E.g. you can use estimatepriority[1] and estimatefee[2] to see how your TX is faring among the others you know about. If you are on the top20 in terms of priority among >50k TX its likely that your TX will get a confirmation without fee. It might not be in the next block though. 21.co does not take the priority into consideration. I guess because most dont even know to calculate (or query) the priority of their TX.