What are the chances that a nonce for one block is a nonce for another? Just to put a cap, let’s say in 1 million blocks, what is the chance that 2 blocks will share the same nonce value? Has it happened before?
Assuming that nonces are randomly distributed (which they should be) and after 1 million blocks that no blocks have the same nonce, the probability of the next block having the same nonce as a block that has already been mined is 1000000/4294967296 = 0.000233, so very low. However as more blocks are being mined, the probability increases. Once there are 4294967296 blocks, the probability of a block sharing a nonce with a different block is guaranteed.

The reasoning for 4294967296 is because the nonce is a 32-bit integer so there are 2^32 possible nonces which is 4294967296.

However, the probability of any 2 blocks having the same nonce is 1/65536 due to the birthday paradox.

There currently have been multiple pairs of blocks that have the same nonce. Some are listed below:

Nnoce: 68229731, blocks [9459, 35238]
Nnoce: 3147243286, blocks [19411, 71181]
Nnoce: 2811235843, blocks [42202, 110904]
Nnoce: 61366272, blocks [100255, 171713]
Nnoce: 74571595, blocks [37187, 176000]
Nnoce: 22876413, blocks [22460, 188416]
Nnoce: 131829089, blocks [40784, 203153]
Nnoce: 2962306894, blocks [136018, 216500]
Nnoce: 3947837747, blocks [222990, 227103]
Nnoce: 194800186, blocks [36506, 243089]
Nnoce: 1388988687, blocks [108366, 251694]
Nnoce: 922984712, blocks [245295, 260005]
Nnoce: 4133916719, blocks [176525, 276110]
Nnoce: 3890141599, blocks [213608, 292419]
Nnoce: 876374308, blocks [18857, 317190]
Nnoce: 70651752, blocks [238831, 322634]
Nnoce: 2359983768, blocks [112651, 325309]
Nnoce: 3421780225, blocks [95525, 328515]
Nnoce: 3787474772, blocks [187117, 346581]
Nnoce: 3956410682, blocks [10506, 350632]
Nnoce: 2756846708, blocks [117891, 355889]
Nnoce: 158953652, blocks [305592, 368094]
Nnoce: 2660238194, blocks [257198, 371219]
Nnoce: 2774929041, blocks [112737, 413142]
Nnoce: 2335903164, blocks [379609, 436786]
Nnoce: 64632759, blocks [60105, 443347]
Nnoce: 2469851573, blocks [225526, 448132]
Nnoce: 84018796, blocks [78009, 453373]
Nnoce: 1935967937, blocks [436055, 454540]
Nnoce: 2900822784, blocks [144802, 457849]
Nnoce: 2434589573, blocks [102268, 467087]
Nnoce: 2965485942, blocks [366411, 481531]
Nnoce: 18390814, blocks [68360, 506618]
Nnoce: 433452460, blocks [157144, 513320]