I interpreted "Is there a probability..." as a statement looking for evidence or a refutation. This sentence is borderline meaningless.
To me, it's incredible people attribute some sort of actual probability to trading noise.Maybe if you're sitting on top of the exchange server it'd be possible. Even if you had an edge in the 5min or 10min I doubt your fills are good enough to capture significant edge.
To OP - You can test this relatively trivially. OHLC data is candlestick data. You can create a label "Up" or "Down" and run a logistic regression it with your predictors being N candle labels and the response being the label of the next candle. Be sure to use proper data processing and splits for out of sample testing. A confusion matrix is probably all you would need to at least sanity test your hypothesis.
You may find it works with some degree of edge (I'd consider anything better than buy and hold, even 0.5% better, an edge). I don't personally have the numbers for you but the system you are describing, "does a previous high predict a second high", has been debated ad nauseum with very little evidence either way. It comes up in TA of Stocks & Commodities probably twice a year. It's probably highly market dependent.