I'm going to assume that "country style ribs" are the ones where you cut them apart first before cooking ... I'd wager a guess that everything is near bone, and a thermometer might have problems with this particular dish. If nothing else, as you can't insert it deeply enough into the thing you're taking a measurement of, there might be enough conduction along the probe for the oven temperature to throw off the reading.
Could you tell us how far the probe was in the meat? I'd assume anything less than about 1/3 the probe might be problematic, with 1/2 or more being better.
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All of that being said, are you sure it's an issue with the placement of the probe, and not a problem with the probe itself?
I've had a number of them go out over the years. I've actually given up on them, and gone back to an instant read thermometer, as I'm up to 4 of the bases (can still use 'em as a timer), and no working probes. (if anyone knows any brands that sell the replacement probes individually, or even better in multi-packs, I'd be willing to go back to using them)
To calibrate -- mix some ice water, and put the probe in there. It should read 32F or 0C. (if it even goes that low, not all do). Boil water, and read the temperature of it, and it should read near 100C or 212F (possibly lower, if you're above sea level). Compare it to another room thermometer after it's been sitting for a bit ... they should read the same.
Don't try to put it into the oven directly ... you could melt the probe ... that's how I lost the first one, so you can't try to compare it to your oven thermometer.
With thin cuts of meat (like chicken breast or a steak), you want to make sure you put the thermometer in to the thin side of the meat so that the whole thermometer goes in to the meat, rather than putting it in through the "top" so that only a little of the thermometer is in the meat. If you're putting it in the top, you can get wildly inaccurate temperatures. Also make sure that the thermometer isn't touching a pan, exposed to air, or touching a bone. Any of those can have a negative effect.
Also, you only need to cook chicken to 74C / 165F. That may be part of the problem in your case.
You may also want to check that your thermometer is accurate. You can stick it in boiling water to check that it reads 100C / 212F (assuming of course it goes up that high).
Best Answer
My experience with metal probes left in meat for the cooking period, if it is not a short cooking time, can give higher than accurate readings unless the item is large enough to bury a high percentage of the probe and still hit that optimal middle of thickest area without hitting bone. If too shallow, the metal can transfer heat itself to the measuring point so give a higher than true internal temp. This tends to happen more often for me with less dense meat. When this is a concern, I would suggest using the probe initially to get to temp, then moving it to a new location when it reads that you have reached temperature. It this thermal transfer via the metal is what is occurring for you, then the new positions should quickly drop to the true temperature and you will know you need addition time. The 2nd point is usually used for less time, so does not tend to have the same false rise.
All of this is predicated on using a calibrated device of a type of probe designed to allow leaving in as mentioned in answers and comments, i.e. not plastic, not instant read, etc. Those designed to remain in are often the ones with flexible cords to an out of oven base for reading and some wireless models. There are those that the readout is not remote, but those have the disadvantage of needing to open the oven.